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 81a290c38..f91f44519 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
@@ -1,25 +1,20 @@
 package space.kscience.kmath.tensors
 
-import space.kscience.kmath.nd.MutableNDBuffer
 import space.kscience.kmath.structures.RealBuffer
 import space.kscience.kmath.structures.array
+import kotlin.math.abs
 import kotlin.math.max
 
 
 public class RealTensor(
-    override val shape: IntArray,
+    shape: IntArray,
     buffer: DoubleArray
-) :
-    TensorStructure<Double>,
-    MutableNDBuffer<Double>(
-        TensorStrides(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]
@@ -40,7 +35,10 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
     override fun zeroesLike(other: RealTensor): RealTensor {
-        TODO("Not yet implemented")
+        // TODO refactor very bad!!!
+        val shape = other.shape
+        val buffer = DoubleArray(other.buffer.size) { 0.0 }
+        return RealTensor(shape, buffer)
     }
 
     override fun ones(shape: IntArray): RealTensor {
@@ -52,7 +50,8 @@ 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 broadcastShapes(vararg shapes: IntArray): IntArray {
@@ -294,12 +293,80 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
     }
 
 
-    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(lu: RealTensor, pivots: IntTensor): Triple<RealTensor, RealTensor, RealTensor> {
+        // todo checks
+        val n = lu.shape[0]
+        val p = zeroesLike(lu)
+        pivots.buffer.array.forEachIndexed { i, pivot ->
+            p[i, pivot] = 1.0
+        }
+        val l = zeroesLike(lu)
+        val u = zeroesLike(lu)
+
+        for (i in 0 until n){
+            for (j in 0 until n){
+                if (i == j) {
+                    l[i, j] = 1.0
+                }
+                if (j < i) {
+                    l[i, j] = lu[i, j]
+                }
+                if (j >= i) {
+                    u[i, j] = lu[i, j]
+                }
+            }
+        }
+        return Triple(p, l, u)
     }
 
     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 ffc0d28cc..ec257e45c 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
@@ -74,11 +74,12 @@ public interface TensorPartialDivisionAlgebra<T, TensorType : TensorStructure<T>
     //https://pytorch.org/docs/stable/generated/torch.log.html
     public fun TensorType.log(): TensorType
 
+    // 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>