diff --git a/examples/build.gradle.kts b/examples/build.gradle.kts
index 77152dc0a..0301e4d67 100644
--- a/examples/build.gradle.kts
+++ b/examples/build.gradle.kts
@@ -92,6 +92,14 @@ benchmark {
         iterationTimeUnit = "ms" // time unity for iterationTime, default is seconds
         include("ExpressionsInterpretersBenchmark")
     }
+
+    configurations.register("matrixInverse") {
+        warmups = 1 // number of warmup iterations
+        iterations = 3 // number of iterations
+        iterationTime = 500 // time in seconds per iteration
+        iterationTimeUnit = "ms" // time unity for iterationTime, default is seconds
+        include("MatrixInverseBenchmark")
+    }
 }
 
 kotlin.sourceSets.all {
diff --git a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/DotBenchmark.kt b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/DotBenchmark.kt
index 8fb0c284e..dbf373929 100644
--- a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/DotBenchmark.kt
+++ b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/DotBenchmark.kt
@@ -6,12 +6,9 @@ import kotlinx.benchmark.Scope
 import kotlinx.benchmark.State
 import space.kscience.kmath.commons.linear.CMLinearSpace
 import space.kscience.kmath.ejml.EjmlLinearSpace
-import space.kscience.kmath.linear.BufferLinearSpace
-import space.kscience.kmath.linear.Matrix
-import space.kscience.kmath.linear.RealLinearSpace
+import space.kscience.kmath.linear.LinearSpace
+import space.kscience.kmath.linear.invoke
 import space.kscience.kmath.operations.RealField
-import space.kscience.kmath.operations.invoke
-import space.kscience.kmath.structures.Buffer
 import kotlin.random.Random
 
 @State(Scope.Benchmark)
@@ -21,8 +18,8 @@ internal class DotBenchmark {
         const val dim = 1000
 
         //creating invertible matrix
-        val matrix1 = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
-        val matrix2 = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
+        val matrix1 = LinearSpace.real.buildMatrix(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
+        val matrix2 = LinearSpace.real.buildMatrix(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
 
         val cmMatrix1 = CMLinearSpace { matrix1.toCM() }
         val cmMatrix2 = CMLinearSpace { matrix2.toCM() }
@@ -33,7 +30,7 @@ internal class DotBenchmark {
 
     @Benchmark
     fun cmDot(blackhole: Blackhole) {
-        CMLinearSpace {
+        CMLinearSpace.run {
             blackhole.consume(cmMatrix1 dot cmMatrix2)
         }
     }
@@ -54,14 +51,14 @@ internal class DotBenchmark {
 
     @Benchmark
     fun bufferedDot(blackhole: Blackhole) {
-        BufferLinearSpace(RealField, Buffer.Companion::real).invoke {
+        LinearSpace.auto(RealField).invoke {
             blackhole.consume(matrix1 dot matrix2)
         }
     }
 
     @Benchmark
     fun realDot(blackhole: Blackhole) {
-        RealLinearSpace {
+        LinearSpace.real {
             blackhole.consume(matrix1 dot matrix2)
         }
     }
diff --git a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ExpressionsInterpretersBenchmark.kt b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ExpressionsInterpretersBenchmark.kt
index 9c150f074..e5cfbf9f6 100644
--- a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ExpressionsInterpretersBenchmark.kt
+++ b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ExpressionsInterpretersBenchmark.kt
@@ -30,7 +30,7 @@ internal class ExpressionsInterpretersBenchmark {
     fun mstExpression(blackhole: Blackhole) {
         val expr = algebra.mstInField {
             val x = bindSymbol(x)
-            x * 2.0 + 2.0 / x - 16.0
+            x * 2.0 + number(2.0) / x - 16.0
         }
 
         invokeAndSum(expr, blackhole)
@@ -40,7 +40,7 @@ internal class ExpressionsInterpretersBenchmark {
     fun asmExpression(blackhole: Blackhole) {
         val expr = algebra.mstInField {
             val x = bindSymbol(x)
-            x * 2.0 + 2.0 / x - 16.0
+            x * 2.0 + number(2.0) / x - 16.0
         }.compile()
 
         invokeAndSum(expr, blackhole)
diff --git a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/MatrixInverseBenchmark.kt
similarity index 75%
rename from examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt
rename to examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/MatrixInverseBenchmark.kt
index 85759d93c..7aa8ac975 100644
--- a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt
+++ b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/MatrixInverseBenchmark.kt
@@ -9,21 +9,22 @@ import space.kscience.kmath.commons.linear.inverse
 import space.kscience.kmath.ejml.EjmlLinearSpace
 import space.kscience.kmath.ejml.inverse
 import space.kscience.kmath.linear.LinearSpace
-import space.kscience.kmath.linear.Matrix
 import space.kscience.kmath.linear.inverseWithLup
-import space.kscience.kmath.linear.real
+import space.kscience.kmath.linear.invoke
 import kotlin.random.Random
 
 @State(Scope.Benchmark)
-internal class LinearAlgebraBenchmark {
+internal class MatrixInverseBenchmark {
     companion object {
         val random = Random(1224)
         const val dim = 100
 
+        private val space = LinearSpace.real
+
         //creating invertible matrix
-        val u = Matrix.real(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
-        val l = Matrix.real(dim, dim) { i, j -> if (i >= j) random.nextDouble() else 0.0 }
-        val matrix = l dot u
+        val u = space.buildMatrix(dim, dim) { i, j -> if (i <= j) random.nextDouble() else 0.0 }
+        val l = space.buildMatrix(dim, dim) { i, j -> if (i >= j) random.nextDouble() else 0.0 }
+        val matrix = space { l dot u }
     }
 
     @Benchmark
diff --git a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
index c48c86af9..0036b615c 100644
--- a/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
+++ b/examples/src/benchmarks/kotlin/space/kscience/kmath/benchmarks/ViktorLogBenchmark.kt
@@ -15,7 +15,7 @@ import space.kscience.kmath.viktor.ViktorNDField
 internal class ViktorLogBenchmark {
     @Benchmark
     fun realFieldLog(blackhole: Blackhole) {
-        with(realField) {
+        with(realNdField) {
             val fortyTwo = produce { 42.0 }
             var res = one
             repeat(n) { res = ln(fortyTwo) }
@@ -47,7 +47,7 @@ internal class ViktorLogBenchmark {
 
         // automatically build context most suited for given type.
         private val autoField = NDAlgebra.auto(RealField, dim, dim)
-        private val realField = NDAlgebra.real(dim, dim)
+        private val realNdField = NDAlgebra.real(dim, dim)
         private val viktorField = ViktorNDField(intArrayOf(dim, dim))
     }
 }
diff --git a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/MstAlgebra.kt b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/MstAlgebra.kt
index 16fdfbeac..5ed39687b 100644
--- a/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/MstAlgebra.kt
+++ b/kmath-ast/src/commonMain/kotlin/space/kscience/kmath/ast/MstAlgebra.kt
@@ -54,7 +54,7 @@ public object MstRing : Ring<MST>, NumbersAddOperations<MST>, ScaleOperations<MS
     public override val one: MST.Numeric = number(1.0)
 
     public override fun number(value: Number): MST.Numeric = MstGroup.number(value)
-    public override fun bindSymbol(value: String): MST.Symbolic = MstGroup.bindSymbol(value)
+    public override fun bindSymbol(value: String): MST.Symbolic = MstAlgebra.bindSymbol(value)
     public override fun add(a: MST, b: MST): MST.Binary = MstGroup.add(a, b)
 
     public override fun scale(a: MST, value: Double): MST.Binary =
@@ -83,7 +83,7 @@ public object MstField : Field<MST>, NumbersAddOperations<MST>, ScaleOperations<
 
     public override val one: MST.Numeric get() = MstRing.one
 
-    public override fun bindSymbol(value: String): MST.Symbolic = MstRing.bindSymbol(value)
+    public override fun bindSymbol(value: String): MST.Symbolic = MstAlgebra.bindSymbol(value)
     public override fun number(value: Number): MST.Numeric = MstRing.number(value)
     public override fun add(a: MST, b: MST): MST.Binary = MstRing.add(a, b)
 
@@ -112,7 +112,7 @@ public object MstExtendedField : ExtendedField<MST>, NumericAlgebra<MST> {
     public override val zero: MST.Numeric get() = MstField.zero
     public override val one: MST.Numeric get() = MstField.one
 
-    public override fun bindSymbol(value: String): MST.Symbolic = MstField.bindSymbol(value)
+    public override fun bindSymbol(value: String): MST.Symbolic = MstAlgebra.bindSymbol(value)
     public override fun number(value: Number): MST.Numeric = MstRing.number(value)
     public override fun sin(arg: MST): MST.Unary = unaryOperationFunction(TrigonometricOperations.SIN_OPERATION)(arg)
     public override fun cos(arg: MST): MST.Unary = unaryOperationFunction(TrigonometricOperations.COS_OPERATION)(arg)
diff --git a/kmath-core/api/kmath-core.api b/kmath-core/api/kmath-core.api
index c1f8d5ec5..38da35d6c 100644
--- a/kmath-core/api/kmath-core.api
+++ b/kmath-core/api/kmath-core.api
@@ -496,7 +496,6 @@ public final class space/kscience/kmath/linear/LinearSpace$Companion {
 }
 
 public final class space/kscience/kmath/linear/LinearSpace$DefaultImpls {
-	public static fun buildVector (Lspace/kscience/kmath/linear/LinearSpace;ILkotlin/jvm/functions/Function2;)Lspace/kscience/kmath/structures/Buffer;
 	public static fun dot (Lspace/kscience/kmath/linear/LinearSpace;Lspace/kscience/kmath/nd/Structure2D;Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/nd/Structure2D;
 	public static fun dot (Lspace/kscience/kmath/linear/LinearSpace;Lspace/kscience/kmath/nd/Structure2D;Lspace/kscience/kmath/structures/Buffer;)Lspace/kscience/kmath/structures/Buffer;
 	public static fun minus (Lspace/kscience/kmath/linear/LinearSpace;Lspace/kscience/kmath/nd/Structure2D;Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/nd/Structure2D;
@@ -511,6 +510,29 @@ public final class space/kscience/kmath/linear/LinearSpace$DefaultImpls {
 	public static fun unaryMinus (Lspace/kscience/kmath/linear/LinearSpace;Lspace/kscience/kmath/structures/Buffer;)Lspace/kscience/kmath/structures/Buffer;
 }
 
+public final class space/kscience/kmath/linear/LinearSpaceKt {
+	public static final fun invoke (Lspace/kscience/kmath/linear/LinearSpace;Lkotlin/jvm/functions/Function1;)Ljava/lang/Object;
+}
+
+public final class space/kscience/kmath/linear/LinearSpaceOverNd : space/kscience/kmath/linear/LinearSpace {
+	public fun <init> (Lspace/kscience/kmath/operations/Ring;Lkotlin/jvm/functions/Function2;)V
+	public fun buildMatrix (IILkotlin/jvm/functions/Function3;)Lspace/kscience/kmath/nd/Structure2D;
+	public fun buildVector (ILkotlin/jvm/functions/Function2;)Lspace/kscience/kmath/structures/Buffer;
+	public fun dot (Lspace/kscience/kmath/nd/Structure2D;Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/nd/Structure2D;
+	public fun dot (Lspace/kscience/kmath/nd/Structure2D;Lspace/kscience/kmath/structures/Buffer;)Lspace/kscience/kmath/structures/Buffer;
+	public fun getElementAlgebra ()Lspace/kscience/kmath/operations/Ring;
+	public fun minus (Lspace/kscience/kmath/nd/Structure2D;Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/nd/Structure2D;
+	public fun minus (Lspace/kscience/kmath/structures/Buffer;Lspace/kscience/kmath/structures/Buffer;)Lspace/kscience/kmath/structures/Buffer;
+	public fun plus (Lspace/kscience/kmath/nd/Structure2D;Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/nd/Structure2D;
+	public fun plus (Lspace/kscience/kmath/structures/Buffer;Lspace/kscience/kmath/structures/Buffer;)Lspace/kscience/kmath/structures/Buffer;
+	public fun times (Ljava/lang/Object;Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/nd/Structure2D;
+	public fun times (Ljava/lang/Object;Lspace/kscience/kmath/structures/Buffer;)Lspace/kscience/kmath/structures/Buffer;
+	public fun times (Lspace/kscience/kmath/nd/Structure2D;Ljava/lang/Object;)Lspace/kscience/kmath/nd/Structure2D;
+	public fun times (Lspace/kscience/kmath/structures/Buffer;Ljava/lang/Object;)Lspace/kscience/kmath/structures/Buffer;
+	public fun unaryMinus (Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/nd/Structure2D;
+	public fun unaryMinus (Lspace/kscience/kmath/structures/Buffer;)Lspace/kscience/kmath/structures/Buffer;
+}
+
 public final class space/kscience/kmath/linear/LupDecomposition : space/kscience/kmath/linear/DeterminantFeature, space/kscience/kmath/linear/LupDecompositionFeature {
 	public fun <init> (Lspace/kscience/kmath/linear/LinearSpace;Lspace/kscience/kmath/operations/Field;Lspace/kscience/kmath/nd/Structure2D;[IZ)V
 	public final fun getContext ()Lspace/kscience/kmath/linear/LinearSpace;
@@ -566,12 +588,12 @@ public final class space/kscience/kmath/linear/MatrixWrapper : space/kscience/km
 	public fun get (II)Ljava/lang/Object;
 	public fun get ([I)Ljava/lang/Object;
 	public fun getColNum ()I
-	public fun getColumns ()Lspace/kscience/kmath/structures/Buffer;
+	public fun getColumns ()Ljava/util/List;
 	public fun getDimension ()I
 	public final fun getFeatures ()Ljava/util/Set;
 	public final fun getOrigin ()Lspace/kscience/kmath/nd/Structure2D;
 	public fun getRowNum ()I
-	public fun getRows ()Lspace/kscience/kmath/structures/Buffer;
+	public fun getRows ()Ljava/util/List;
 	public fun getShape ()[I
 	public fun hashCode ()I
 	public fun toString ()Ljava/lang/String;
@@ -622,11 +644,11 @@ public final class space/kscience/kmath/linear/VirtualMatrix : space/kscience/km
 	public fun get (II)Ljava/lang/Object;
 	public fun get ([I)Ljava/lang/Object;
 	public fun getColNum ()I
-	public fun getColumns ()Lspace/kscience/kmath/structures/Buffer;
+	public fun getColumns ()Ljava/util/List;
 	public fun getDimension ()I
 	public final fun getGenerator ()Lkotlin/jvm/functions/Function2;
 	public fun getRowNum ()I
-	public fun getRows ()Lspace/kscience/kmath/structures/Buffer;
+	public fun getRows ()Ljava/util/List;
 	public fun getShape ()[I
 	public fun hashCode ()I
 }
@@ -678,11 +700,11 @@ public final class space/kscience/kmath/nd/BufferNDAlgebra$DefaultImpls {
 
 public final class space/kscience/kmath/nd/BufferNDAlgebraKt {
 	public static final fun field (Lspace/kscience/kmath/nd/NDAlgebra$Companion;Lspace/kscience/kmath/operations/Field;Lkotlin/jvm/functions/Function2;[I)Lspace/kscience/kmath/nd/BufferedNDField;
+	public static final fun group (Lspace/kscience/kmath/nd/NDAlgebra$Companion;Lspace/kscience/kmath/operations/Group;Lkotlin/jvm/functions/Function2;[I)Lspace/kscience/kmath/nd/BufferedNDGroup;
 	public static final fun ndField (Lspace/kscience/kmath/operations/Field;Lkotlin/jvm/functions/Function2;[ILkotlin/jvm/functions/Function1;)Ljava/lang/Object;
+	public static final fun ndGroup (Lspace/kscience/kmath/operations/Group;Lkotlin/jvm/functions/Function2;[ILkotlin/jvm/functions/Function1;)Ljava/lang/Object;
 	public static final fun ndRing (Lspace/kscience/kmath/operations/Ring;Lkotlin/jvm/functions/Function2;[ILkotlin/jvm/functions/Function1;)Ljava/lang/Object;
-	public static final fun ndSpace (Lspace/kscience/kmath/operations/Group;Lkotlin/jvm/functions/Function2;[ILkotlin/jvm/functions/Function1;)Ljava/lang/Object;
 	public static final fun ring (Lspace/kscience/kmath/nd/NDAlgebra$Companion;Lspace/kscience/kmath/operations/Ring;Lkotlin/jvm/functions/Function2;[I)Lspace/kscience/kmath/nd/BufferedNDRing;
-	public static final fun space (Lspace/kscience/kmath/nd/NDAlgebra$Companion;Lspace/kscience/kmath/operations/Group;Lkotlin/jvm/functions/Function2;[I)Lspace/kscience/kmath/nd/BufferedNDGroup;
 }
 
 public class space/kscience/kmath/nd/BufferedNDField : space/kscience/kmath/nd/BufferedNDRing, space/kscience/kmath/nd/NDField {
@@ -1103,9 +1125,9 @@ public abstract interface class space/kscience/kmath/nd/Structure2D : space/ksci
 	public abstract fun get (II)Ljava/lang/Object;
 	public abstract fun get ([I)Ljava/lang/Object;
 	public abstract fun getColNum ()I
-	public abstract fun getColumns ()Lspace/kscience/kmath/structures/Buffer;
+	public abstract fun getColumns ()Ljava/util/List;
 	public abstract fun getRowNum ()I
-	public abstract fun getRows ()Lspace/kscience/kmath/structures/Buffer;
+	public abstract fun getRows ()Ljava/util/List;
 	public abstract fun getShape ()[I
 }
 
@@ -1115,9 +1137,9 @@ public final class space/kscience/kmath/nd/Structure2D$Companion {
 public final class space/kscience/kmath/nd/Structure2D$DefaultImpls {
 	public static fun elements (Lspace/kscience/kmath/nd/Structure2D;)Lkotlin/sequences/Sequence;
 	public static fun get (Lspace/kscience/kmath/nd/Structure2D;[I)Ljava/lang/Object;
-	public static fun getColumns (Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/structures/Buffer;
+	public static fun getColumns (Lspace/kscience/kmath/nd/Structure2D;)Ljava/util/List;
 	public static fun getDimension (Lspace/kscience/kmath/nd/Structure2D;)I
-	public static fun getRows (Lspace/kscience/kmath/nd/Structure2D;)Lspace/kscience/kmath/structures/Buffer;
+	public static fun getRows (Lspace/kscience/kmath/nd/Structure2D;)Ljava/util/List;
 	public static fun getShape (Lspace/kscience/kmath/nd/Structure2D;)[I
 }
 
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
index 4a9d2c9b3..b0331bdea 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpace.kt
@@ -33,8 +33,7 @@ public interface LinearSpace<T : Any, out A : Ring<T>> {
     /**
      * Produces a point compatible with matrix space (and possibly optimized for it).
      */
-    public fun buildVector(size: Int, initializer: A.(Int) -> T): Vector<T> =
-        buildMatrix(1, size) { _, j -> initializer(j) }.as1D()
+    public fun buildVector(size: Int, initializer: A.(Int) -> T): Vector<T>
 
     public operator fun Matrix<T>.unaryMinus(): Matrix<T> = buildMatrix(rowNum, colNum) { i, j ->
         -get(i, j)
@@ -154,7 +153,7 @@ public interface LinearSpace<T : Any, out A : Ring<T>> {
 
     /**
      * Gets a feature from the matrix. This function may return some additional features to
-     * [space.kscience.kmath.nd.NDStructure.getFeature].
+     * [group.kscience.kmath.nd.NDStructure.getFeature].
      *
      * @param F the type of feature.
      * @param m the matrix.
@@ -172,16 +171,7 @@ public interface LinearSpace<T : Any, out A : Ring<T>> {
         public fun <T : Any, A : Ring<T>> buffered(
             algebra: A,
             bufferFactory: BufferFactory<T> = Buffer.Companion::boxing,
-        ): LinearSpace<T, A> = object : LinearSpace<T, A> {
-            override val elementAlgebra: A = algebra
-
-            override fun buildMatrix(
-                rows: Int, columns: Int,
-                initializer: A.(i: Int, j: Int) -> T,
-            ): Matrix<T> = NDStructure.buffered(intArrayOf(rows, columns), bufferFactory) { (i, j) ->
-                algebra.initializer(i, j)
-            }.as2D()
-        }
+        ): LinearSpace<T, A> = LinearSpaceOverNd(algebra,bufferFactory)
 
         public val real: LinearSpace<Double, RealField> = buffered(RealField, Buffer.Companion::real)
 
@@ -193,9 +183,11 @@ public interface LinearSpace<T : Any, out A : Ring<T>> {
     }
 }
 
+public operator fun <LS : LinearSpace<*, *>, R> LS.invoke(block: LS.() -> R): R = run(block)
+
 /**
  * Gets a feature from the matrix. This function may return some additional features to
- * [space.kscience.kmath.nd.NDStructure.getFeature].
+ * [group.kscience.kmath.nd.NDStructure.getFeature].
  *
  * @param T the type of items in the matrices.
  * @param M the type of operated matrices.
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpaceOverNd.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpaceOverNd.kt
new file mode 100644
index 000000000..6a82f37ec
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/linear/LinearSpaceOverNd.kt
@@ -0,0 +1,85 @@
+package space.kscience.kmath.linear
+
+import space.kscience.kmath.nd.*
+import space.kscience.kmath.operations.Ring
+import space.kscience.kmath.operations.invoke
+import space.kscience.kmath.structures.Buffer
+import space.kscience.kmath.structures.BufferFactory
+import space.kscience.kmath.structures.VirtualBuffer
+import space.kscience.kmath.structures.indices
+
+
+public class LinearSpaceOverNd<T : Any, A : Ring<T>>(
+    override val elementAlgebra: A,
+    private val bufferFactory: BufferFactory<T>,
+) : LinearSpace<T, A> {
+
+    private fun ndRing(
+        rows: Int,
+        cols: Int,
+    ): BufferedNDRing<T, A> = NDAlgebra.ring(elementAlgebra, bufferFactory, rows, cols)
+
+    override fun buildMatrix(rows: Int, columns: Int, initializer: A.(i: Int, j: Int) -> T): Matrix<T> =
+        ndRing(rows, columns).produce { (i, j) -> elementAlgebra.initializer(i, j) }.as2D()
+
+    override fun buildVector(size: Int, initializer: A.(Int) -> T): Vector<T> =
+        bufferFactory(size) { elementAlgebra.initializer(it) }
+
+    override fun Matrix<T>.unaryMinus(): Matrix<T> = ndRing(rowNum, colNum).run {
+        unwrap().map { -it }.as2D()
+    }
+
+    override fun Matrix<T>.plus(other: Matrix<T>): Matrix<T> = ndRing(rowNum, colNum).run {
+        require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::plus. Expected $shape but found ${other.shape}" }
+        unwrap().plus(other.unwrap()).as2D()
+    }
+
+    override fun Matrix<T>.minus(other: Matrix<T>): Matrix<T> = ndRing(rowNum, colNum).run {
+        require(shape.contentEquals(other.shape)) { "Shape mismatch on Matrix::plus. Expected $shape but found ${other.shape}" }
+        unwrap().minus(other.unwrap()).as2D()
+    }
+
+    private fun Buffer<T>.linearize() = if (this is VirtualBuffer) {
+        buildVector(size) { get(it) }
+    } else {
+        this
+    }
+
+    override fun Matrix<T>.dot(other: Matrix<T>): Matrix<T> {
+        require(colNum == other.rowNum) { "Matrix dot operation dimension mismatch: ($rowNum, $colNum) x (${other.rowNum}, ${other.colNum})" }
+        return elementAlgebra {
+            val rows = this@dot.rows.map{it.linearize()}
+            val columns = other.columns.map { it.linearize() }
+            //TODO optimize buffers
+            buildMatrix(rowNum, other.colNum) { i, j ->
+                val r = rows[i]
+                val c = columns[j]
+                var res = zero
+                for (l in r.indices) {
+                    res += r[l] * c[l]
+                }
+                res
+            }
+        }
+    }
+
+    override fun Matrix<T>.dot(vector: Vector<T>): Vector<T> {
+        require(colNum == vector.size) { "Matrix dot vector operation dimension mismatch: ($rowNum, $colNum) x (${vector.size})" }
+        return elementAlgebra {
+            val rows = this@dot.rows
+            //TODO optimize buffers
+            buildVector(rowNum) { i ->
+                val r = rows[i]
+                var res = zero
+                for (j in r.indices) {
+                    res += r[j] * vector[j]
+                }
+                res
+            }
+        }
+    }
+
+    override fun Matrix<T>.times(value: T): Matrix<T> = ndRing(rowNum, colNum).run {
+        unwrap().map { it * value }.as2D()
+    }
+}
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferNDAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferNDAlgebra.kt
index 58d1ea7b1..bce3a0830 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferNDAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/BufferNDAlgebra.kt
@@ -79,20 +79,20 @@ public open class BufferedNDField<T, R : Field<T>>(
     override fun scale(a: NDStructure<T>, value: Double): NDStructure<T> = a.map { it * value }
 }
 
-// space factories
-public fun <T, A : Group<T>> NDAlgebra.Companion.space(
+// group factories
+public fun <T, A : Group<T>> NDAlgebra.Companion.group(
     space: A,
     bufferFactory: BufferFactory<T>,
     vararg shape: Int,
 ): BufferedNDGroup<T, A> = BufferedNDGroup(shape, space, bufferFactory)
 
-public inline fun <T, A : Group<T>, R> A.ndSpace(
+public inline fun <T, A : Group<T>, R> A.ndGroup(
     noinline bufferFactory: BufferFactory<T>,
     vararg shape: Int,
     action: BufferedNDGroup<T, A>.() -> R,
 ): R {
     contract { callsInPlace(action, InvocationKind.EXACTLY_ONCE) }
-    return NDAlgebra.space(this, bufferFactory, *shape).run(action)
+    return NDAlgebra.group(this, bufferFactory, *shape).run(action)
 }
 
 //ring factories
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt
index c54bfeed9..1335a4933 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure1D.kt
@@ -45,14 +45,12 @@ private inline class Buffer1DWrapper<T>(val buffer: Buffer<T>) : Structure1D<T>
 /**
  * Represent a [NDStructure] as [Structure1D]. Throw error in case of dimension mismatch
  */
-public fun <T> NDStructure<T>.as1D(): Structure1D<T> = if (shape.size == 1) {
+public fun <T> NDStructure<T>.as1D(): Structure1D<T> = this as? Structure1D<T> ?: if (shape.size == 1) {
     when (this) {
-        is Structure1DWrapper -> this
         is NDBuffer -> Buffer1DWrapper(this.buffer)
         else -> Structure1DWrapper(this)
     }
-} else
-    error("Can't create 1d-structure from ${shape.size}d-structure")
+} else error("Can't create 1d-structure from ${shape.size}d-structure")
 
 /**
  * Represent this buffer as 1D structure
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt
index 09c830646..e9f8234e5 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/nd/Structure2D.kt
@@ -26,14 +26,14 @@ public interface Structure2D<T> : NDStructure<T> {
     /**
      * The buffer of rows of this structure. It gets elements from the structure dynamically.
      */
-    public val rows: Buffer<Buffer<T>>
-        get() = VirtualBuffer(rowNum) { i -> VirtualBuffer(colNum) { j -> get(i, j) } }
+    public val rows: List<Buffer<T>>
+        get() = List(rowNum) { i -> VirtualBuffer(colNum) { j -> get(i, j) } }
 
     /**
      * The buffer of columns of this structure. It gets elements from the structure dynamically.
      */
-    public val columns: Buffer<Buffer<T>>
-        get() = VirtualBuffer(colNum) { j -> VirtualBuffer(rowNum) { i -> get(i, j) } }
+    public val columns: List<Buffer<T>>
+        get() = List(colNum) { j -> VirtualBuffer(rowNum) { i -> get(i, j) } }
 
     /**
      * Retrieves an element from the structure by two indices.
@@ -75,20 +75,15 @@ private class Structure2DWrapper<T>(val structure: NDStructure<T>) : Structure2D
 
     override fun equals(other: Any?): Boolean = structure == other
 
-    override fun hashCode(): Int  = structure.hashCode()
+    override fun hashCode(): Int = structure.hashCode()
 }
 
 /**
  * Represent a [NDStructure] as [Structure1D]. Throw error in case of dimension mismatch
  */
-public fun <T> NDStructure<T>.as2D(): Structure2D<T> = if (shape.size == 2)
-    Structure2DWrapper(this)
-else
-    error("Can't create 2d-structure from ${shape.size}d-structure")
+public fun <T> NDStructure<T>.as2D(): Structure2D<T> = this as? Structure2D<T> ?: when (shape.size) {
+    2 -> Structure2DWrapper(this)
+    else -> error("Can't create 2d-structure from ${shape.size}d-structure")
+}
 
-/**
- * Alias for [Structure2D] with more familiar name.
- *
- * @param T the type of items in the matrix.
- */
-public typealias Matrix<T> = Structure2D<T>
+internal fun <T> Structure2D<T>.unwrap(): NDStructure<T> = if (this is Structure2DWrapper) structure else this
\ No newline at end of file
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt
index d9e37ebd8..0910b2034 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/BufferAccessor2D.kt
@@ -13,10 +13,10 @@ internal class BufferAccessor2D<T : Any>(
     public val colNum: Int,
     val factory: MutableBufferFactory<T>,
 ) {
-    public operator fun Buffer<T>.get(i: Int, j: Int): T = get(i + colNum * j)
+    public operator fun Buffer<T>.get(i: Int, j: Int): T = get(i*colNum + j)
 
     public operator fun MutableBuffer<T>.set(i: Int, j: Int, value: T) {
-        set(i + colNum * j, value)
+        set(i*colNum + j, value)
     }
 
     public inline fun create(crossinline init: (i: Int, j: Int) -> T): MutableBuffer<T> =
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferOperation.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferOperation.kt
new file mode 100644
index 000000000..459136631
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/structures/bufferOperation.kt
@@ -0,0 +1,7 @@
+package space.kscience.kmath.structures
+
+
+public inline fun <T : Any, reified R : Any> Buffer<T>.map(
+    bufferFactory: BufferFactory<R> = Buffer.Companion::auto,
+    crossinline block: (T) -> R,
+): Buffer<R> = bufferFactory(size) { block(get(it)) }
\ No newline at end of file
diff --git a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/linear/RealLUSolverTest.kt b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/linear/RealLUSolverTest.kt
index 704f91998..fb90b5e11 100644
--- a/kmath-core/src/commonTest/kotlin/space/kscience/kmath/linear/RealLUSolverTest.kt
+++ b/kmath-core/src/commonTest/kotlin/space/kscience/kmath/linear/RealLUSolverTest.kt
@@ -19,13 +19,13 @@ class RealLUSolverTest {
         LinearSpace.real.run {
             val matrix = matrix(2,2)(
                 3.0, 1.0,
-                1.0, 3.0
+                2.0, 3.0
             )
 
             val lup = lup(matrix)
 
             //Check determinant
-            assertEquals(8.0, lup.determinant)
+            assertEquals(7.0, lup.determinant)
 
             assertEquals(lup.p dot matrix, lup.l dot lup.u)
         }
diff --git a/kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/EjmlLinearSpace.kt b/kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/EjmlLinearSpace.kt
index 57ce977fd..2d3a928a6 100644
--- a/kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/EjmlLinearSpace.kt
+++ b/kmath-ejml/src/main/kotlin/space/kscience/kmath/ejml/EjmlLinearSpace.kt
@@ -5,14 +5,13 @@ import space.kscience.kmath.linear.*
 import space.kscience.kmath.misc.UnstableKMathAPI
 import space.kscience.kmath.nd.getFeature
 import space.kscience.kmath.operations.RealField
-import space.kscience.kmath.operations.ScaleOperations
 
 /**
  * Represents context of basic operations operating with [EjmlMatrix].
  *
  * @author Iaroslav Postovalov
  */
-public object EjmlLinearSpace : LinearSpace<Double, RealField>, ScaleOperations<Matrix<Double>> {
+public object EjmlLinearSpace : LinearSpace<Double, RealField> {
 
     override val elementAlgebra: RealField get() = RealField
 
@@ -50,7 +49,7 @@ public object EjmlLinearSpace : LinearSpace<Double, RealField>, ScaleOperations<
     private fun SimpleMatrix.wrapMatrix() = EjmlMatrix(this)
     private fun SimpleMatrix.wrapVector() = EjmlVector(this)
 
-    override fun Matrix<Double>.unaryMinus(): Matrix<Double> = this * (-1)
+    override fun Matrix<Double>.unaryMinus(): Matrix<Double> = this * (-1.0)
 
     public override fun Matrix<Double>.dot(other: Matrix<Double>): EjmlMatrix =
         EjmlMatrix(toEjml().origin.mult(other.toEjml().origin))
@@ -61,9 +60,6 @@ public object EjmlLinearSpace : LinearSpace<Double, RealField>, ScaleOperations<
     public override operator fun Matrix<Double>.minus(other: Matrix<Double>): EjmlMatrix =
         (toEjml().origin - other.toEjml().origin).wrapMatrix()
 
-    public override fun scale(a: Matrix<Double>, value: Double): EjmlMatrix =
-        a.toEjml().origin.scale(value).wrapMatrix()
-
     public override operator fun Matrix<Double>.times(value: Double): EjmlMatrix =
         toEjml().origin.scale(value).wrapMatrix()
 
diff --git a/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/dot.kt b/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/dot.kt
index 1a7c1213c..0bc5c111b 100644
--- a/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/dot.kt
+++ b/kmath-for-real/src/commonMain/kotlin/space/kscience/kmath/real/dot.kt
@@ -1,7 +1,7 @@
 package space.kscience.kmath.real
 
 import space.kscience.kmath.linear.LinearSpace
-import space.kscience.kmath.nd.Matrix
+import space.kscience.kmath.linear.Matrix
 
 
 /**