diff --git a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt
index e7345163f..68961a2db 100644
--- a/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt
+++ b/kmath-core/src/commonMain/kotlin/scientifik/kmath/linear/LinearAlgrebra.kt
@@ -55,6 +55,26 @@ abstract class MatrixSpace<T : Any>(val rows: Int, val columns: Int, val field:
             (0 until a.columns).asSequence().map { k -> field.multiply(a[i, k], b[k, j]) }.reduce { first, second -> field.add(first, second) }
         }
     }
+
+    override fun equals(other: Any?): Boolean {
+        if (this === other) return true
+        if (other !is MatrixSpace<*>) return false
+
+        if (rows != other.rows) return false
+        if (columns != other.columns) return false
+        if (field != other.field) return false
+
+        return true
+    }
+
+    override fun hashCode(): Int {
+        var result = rows
+        result = 31 * result + columns
+        result = 31 * result + field.hashCode()
+        return result
+    }
+
+
 }
 
 infix fun <T : Any> Matrix<T>.dot(b: Matrix<T>): Matrix<T> = this.context.multiply(this, b)
@@ -90,8 +110,38 @@ interface Matrix<T : Any> : SpaceElement<Matrix<T>, MatrixSpace<T>> {
     }
 
     companion object {
-        fun <T : Any> one(rows: Int, columns: Int, field: Field<T>): Matrix<T> {
-            return matrix(rows, columns, field) { i, j -> if (i == j) field.one else field.zero }
+
+        /**
+         * Create [ArrayMatrix] with custom field
+         */
+        fun <T : Any> of(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) =
+                ArrayMatrix(ArrayMatrixSpace(rows, columns, field), initializer)
+
+        /**
+         * Create [ArrayMatrix] of doubles. The implementation in general should be faster than generic one due to boxing.
+         */
+        fun ofReal(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
+                ArrayMatrix(ArrayMatrixSpace(rows, columns, DoubleField, realNDFieldFactory), initializer)
+
+        /**
+         * Create a diagonal value matrix. By default value equals [Field.one].
+         */
+        fun <T : Any> diagonal(rows: Int, columns: Int, field: Field<T>, values: (Int) -> T = { field.one }): Matrix<T> {
+            return of(rows, columns, field) { i, j -> if (i == j) values(i) else field.zero }
+        }
+
+        /**
+         * Equality check on two generic matrices
+         */
+        fun equals(mat1: Matrix<*>, mat2: Matrix<*>): Boolean {
+            if (mat1 === mat2) return true
+            if (mat1.context != mat2.context) return false
+            for (i in 0 until mat1.rows) {
+                for (j in 0 until mat2.columns) {
+                    if (mat1[i, j] != mat2[i, j]) return false
+                }
+            }
+            return true
         }
     }
 }
@@ -117,6 +167,30 @@ interface Vector<T : Any> : SpaceElement<Vector<T>, VectorSpace<T>> {
         get() = context.size
 
     operator fun get(i: Int): T
+
+    companion object {
+        /**
+         * Create vector with custom field
+         */
+        fun <T : Any> of(size: Int, field: Field<T>, initializer: (Int) -> T) =
+                ArrayVector(ArrayVectorSpace(size, field), initializer)
+
+        /**
+         * Create vector of [Double]
+         */
+        fun ofReal(size: Int, initializer: (Int) -> Double) =
+                ArrayVector(ArrayVectorSpace(size, DoubleField, realNDFieldFactory), initializer)
+
+
+        fun equals(v1: Vector<*>, v2: Vector<*>): Boolean {
+            if (v1 === v2) return true
+            if (v1.context != v2.context) return false
+            for (i in 0 until v2.size) {
+                if (v1[i] != v2[i]) return false
+            }
+            return true
+        }
+    }
 }
 
 
@@ -195,40 +269,15 @@ class ArrayVector<T : Any> internal constructor(override val context: ArrayVecto
 interface LinearSolver<T : Any> {
     fun solve(a: Matrix<T>, b: Matrix<T>): Matrix<T>
     fun solve(a: Matrix<T>, b: Vector<T>): Vector<T> = solve(a, b.toMatrix()).toVector()
-    fun inverse(a: Matrix<T>): Matrix<T> = solve(a, Matrix.one(a.rows, a.columns, a.context.field))
+    fun inverse(a: Matrix<T>): Matrix<T> = solve(a, Matrix.diagonal(a.rows, a.columns, a.context.field))
 }
 
-/**
- * Create vector with custom field
- */
-fun <T : Any> vector(size: Int, field: Field<T>, initializer: (Int) -> T) =
-        ArrayVector(ArrayVectorSpace(size, field), initializer)
-
-/**
- * Create vector of [Double]
- */
-fun realVector(size: Int, initializer: (Int) -> Double) =
-        ArrayVector(ArrayVectorSpace(size, DoubleField, realNDFieldFactory), initializer)
-
 /**
  * Convert vector to array (copying content of array)
  */
-fun <T : Any> Array<T>.asVector(field: Field<T>) = vector(size, field) { this[it] }
-
-fun DoubleArray.asVector() = realVector(this.size) { this[it] }
-
-/**
- * Create [ArrayMatrix] with custom field
- */
-fun <T : Any> matrix(rows: Int, columns: Int, field: Field<T>, initializer: (Int, Int) -> T) =
-        ArrayMatrix(ArrayMatrixSpace(rows, columns, field), initializer)
-
-/**
- * Create [ArrayMatrix] of doubles.
- */
-fun realMatrix(rows: Int, columns: Int, initializer: (Int, Int) -> Double) =
-        ArrayMatrix(ArrayMatrixSpace(rows, columns, DoubleField, realNDFieldFactory), initializer)
+fun <T : Any> Array<T>.toVector(field: Field<T>) = Vector.of(size, field) { this[it] }
 
+fun DoubleArray.toVector() = Vector.ofReal(this.size) { this[it] }
 
 /**
  * Convert matrix to vector if it is possible
@@ -243,7 +292,7 @@ fun <T : Any> Matrix<T>.toVector(): Vector<T> {
 //                //Generic vector
 //                vector(rows, context.field) { get(it, 0) }
 //            }
-            vector(rows, context.field) { get(it, 0) }
+            Vector.of(rows, context.field) { get(it, 0) }
         }
         else -> error("Can't convert matrix with more than one column to vector")
     }
@@ -257,6 +306,6 @@ fun <T : Any> Vector<T>.toMatrix(): Matrix<T> {
 //        //Generic vector
 //        matrix(size, 1, context.field) { i, j -> get(i) }
 //    }
-    return matrix(size, 1, context.field) { i, j -> get(i) }
+    return Matrix.of(size, 1, context.field) { i, j -> get(i) }
 }
 
diff --git a/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt b/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
index d2237b80a..472d5262f 100644
--- a/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
+++ b/kmath-core/src/commonTest/kotlin/scientifik/kmath/linear/RealLUSolverTest.kt
@@ -2,13 +2,20 @@ package scientifik.kmath.linear
 
 import scientifik.kmath.operations.DoubleField
 import kotlin.test.Test
-import kotlin.test.assertEquals
+import kotlin.test.assertTrue
 
 class RealLUSolverTest {
     @Test
-    fun testInvert() {
-        val matrix = Matrix.one(2, 2, DoubleField)
+    fun testInvertOne() {
+        val matrix = Matrix.diagonal(2, 2, DoubleField)
         val inverted = RealLUSolver.inverse(matrix)
-        assertEquals(1.0, inverted[0, 0])
+        assertTrue { Matrix.equals(matrix,inverted) }
     }
+
+//    @Test
+//    fun testInvert() {
+//        val matrix = realMatrix(2,2){}
+//        val inverted = RealLUSolver.inverse(matrix)
+//        assertTrue { Matrix.equals(matrix,inverted) }
+//    }
 }
\ No newline at end of file