diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/BufferTensor.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/BufferTensor.kt
deleted file mode 100644
index 817c51f11..000000000
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/BufferTensor.kt
+++ /dev/null
@@ -1,33 +0,0 @@
-package space.kscience.kmath.tensors
-
-import space.kscience.kmath.linear.BufferMatrix
-import space.kscience.kmath.linear.RealMatrixContext.toBufferMatrix
-import space.kscience.kmath.nd.Matrix
-import space.kscience.kmath.nd.MutableNDBuffer
-import space.kscience.kmath.nd.Structure2D
-import space.kscience.kmath.nd.as2D
-import space.kscience.kmath.structures.Buffer
-import space.kscience.kmath.structures.BufferAccessor2D
-import space.kscience.kmath.structures.MutableBuffer
-import space.kscience.kmath.structures.toList
-
-public open class BufferTensor<T>(
-    override val shape: IntArray,
-    buffer: MutableBuffer<T>
-) :
-    TensorStructure<T>,
-    MutableNDBuffer<T>(
-        TensorStrides(shape),
-        buffer
-    )
-
-
-public fun <T : Any> BufferTensor<T>.toBufferMatrix(): BufferMatrix<T> {
-    return BufferMatrix(shape[0], shape[1], this.buffer)
-}
-
-// T???
-public fun BufferMatrix<Double>.BufferTensor(): BufferTensor<Double> {
-    return BufferTensor(intArrayOf(rowNum, colNum),  BufferAccessor2D(rowNum, colNum, Buffer.Companion::real).create(this))
-}
-
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/BufferedTensor.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/BufferedTensor.kt
new file mode 100644
index 000000000..9ffe2db61
--- /dev/null
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/BufferedTensor.kt
@@ -0,0 +1,33 @@
+package space.kscience.kmath.tensors
+
+import space.kscience.kmath.linear.BufferMatrix
+import space.kscience.kmath.nd.MutableNDBuffer
+import space.kscience.kmath.structures.*
+import space.kscience.kmath.structures.BufferAccessor2D
+
+public open class BufferedTensor<T>(
+    override val shape: IntArray,
+    buffer: MutableBuffer<T>
+) :
+    TensorStructure<T>,
+    MutableNDBuffer<T>(
+        TensorStrides(shape),
+        buffer
+    ) {
+
+    public operator fun get(i: Int, j: Int): T{
+            check(this.dimension == 2) {"Not matrix"}
+            return this[intArrayOf(i, j)]
+    }
+
+    public operator fun set(i: Int, j: Int, value: T): Unit{
+        check(this.dimension == 2) {"Not matrix"}
+        this[intArrayOf(i, j)] = value
+    }
+
+}
+
+public class IntTensor(
+    shape: IntArray,
+    buffer: IntArray
+) : BufferedTensor<Int>(shape, IntBuffer(buffer))
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
index e38056097..3e21a3a98 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/RealTensorAlgebra.kt
@@ -1,24 +1,19 @@
 package space.kscience.kmath.tensors
 
-import space.kscience.kmath.linear.BufferMatrix
-import space.kscience.kmath.linear.RealMatrixContext.toBufferMatrix
-import space.kscience.kmath.nd.MutableNDBuffer
-import space.kscience.kmath.nd.as2D
-import space.kscience.kmath.structures.Buffer
 import space.kscience.kmath.structures.RealBuffer
 import space.kscience.kmath.structures.array
-import space.kscience.kmath.structures.toList
+import kotlin.math.abs
 
 
 public class RealTensor(
     shape: IntArray,
     buffer: DoubleArray
-) : BufferTensor<Double>(shape, RealBuffer(buffer))
+) : BufferedTensor<Double>(shape, RealBuffer(buffer))
 
 public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor> {
 
     override fun RealTensor.value(): Double {
-        check(this.shape contentEquals  intArrayOf(1)) {
+        check(this.shape contentEquals intArrayOf(1)) {
             "Inconsistent value for tensor of shape ${shape.toList()}"
         }
         return this.buffer.array[0]
@@ -51,7 +46,8 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
     override fun RealTensor.copy(): RealTensor {
-        TODO("Not yet implemented")
+        // should be rework as soon as copy() method for NDBuffer will be available
+        return RealTensor(this.shape, this.buffer.array.copyOf())
     }
 
     override fun Double.plus(other: RealTensor): RealTensor {
@@ -249,12 +245,59 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
         TODO("Not yet implemented")
     }
 
-    override fun RealTensor.lu(): Pair<RealTensor, RealTensor> {
-        TODO()
+    override fun RealTensor.lu(): Pair<RealTensor, IntTensor> {
+        // todo checks
+        val lu = this.copy()
+        val m = this.shape[0]
+        val pivot = IntArray(m)
+
+
+        // Initialize permutation array and parity
+        for (row in 0 until m) pivot[row] = row
+        var even = true
+
+        for (i in 0 until m) {
+            var maxA = -1.0
+            var iMax = i
+
+            for (k in i until m) {
+                val absA = abs(lu[k, i])
+                if (absA > maxA) {
+                    maxA = absA
+                    iMax = k
+                }
+            }
+
+            //todo check singularity
+
+            if (iMax != i) {
+
+                val j = pivot[i]
+                pivot[i] = pivot[iMax]
+                pivot[iMax] = j
+                even != even
+
+                for (k in 0 until m) {
+                    val tmp = lu[i, k]
+                    lu[i, k] = lu[iMax, k]
+                    lu[iMax, k] = tmp
+                }
+
+            }
+
+            for (j in i + 1 until m) {
+                lu[j, i] /= lu[i, i]
+                for (k in i + 1 until m) {
+                    lu[j, k] -= lu[j, i] * lu[i, k]
+                }
+            }
+        }
+        return Pair(lu, IntTensor(intArrayOf(m), pivot))
     }
 
-    override fun luUnpack(A_LU: RealTensor, pivots: RealTensor): Triple<RealTensor, RealTensor, RealTensor> {
-        TODO("Not yet implemented")
+    override fun luUnpack(A_LU: RealTensor, pivots: IntTensor): Triple<RealTensor, RealTensor, RealTensor> {
+        // todo checks
+
     }
 
     override fun RealTensor.svd(): Triple<RealTensor, RealTensor, RealTensor> {
diff --git a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt
index 6f42623e0..0dbcae044 100644
--- a/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt
+++ b/kmath-core/src/commonMain/kotlin/space/kscience/kmath/tensors/TensorAlgebra.kt
@@ -78,11 +78,12 @@ public interface TensorPartialDivisionAlgebra<T, TensorType : TensorStructure<T>
     public fun TensorType.log(): TensorType
     public fun TensorType.logAssign(): Unit
 
+    // todo change type of pivots
     //https://pytorch.org/docs/stable/generated/torch.lu.html
-    public fun TensorType.lu(): Pair<TensorType, TensorType>
+    public fun TensorType.lu(): Pair<TensorType, IntTensor>
 
     //https://pytorch.org/docs/stable/generated/torch.lu_unpack.html
-    public fun luUnpack(A_LU: TensorType, pivots: TensorType): Triple<TensorType, TensorType, TensorType>
+    public fun luUnpack(A_LU: TensorType, pivots: IntTensor): Triple<TensorType, TensorType, TensorType>
 
     //https://pytorch.org/docs/stable/generated/torch.svd.html
     public fun TensorType.svd(): Triple<TensorType, TensorType, TensorType>