diff --git a/examples/src/main/kotlin/space/kscience/kmath/tensors/LinearSystemSolvingWithLUP.kt b/examples/src/main/kotlin/space/kscience/kmath/tensors/LinearSystemSolvingWithLUP.kt
index 526b6781f..38d8c1437 100644
--- a/examples/src/main/kotlin/space/kscience/kmath/tensors/LinearSystemSolvingWithLUP.kt
+++ b/examples/src/main/kotlin/space/kscience/kmath/tensors/LinearSystemSolvingWithLUP.kt
@@ -42,8 +42,7 @@ fun main () {
         // solve `Ax = b` system using LUP decomposition
 
         // get P, L, U such that PA = LU
-        val (lu, pivots) = a.lu()
-        val (p, l, u) = luPivot(lu, pivots)
+        val (p, l, u) = a.lu()
 
         // check that P is permutation matrix
         println("P:\n$p")
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt
index 7a19c5d5a..bcbb52a1b 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/api/LinearOpsTensorAlgebra.kt
@@ -60,23 +60,17 @@ public interface LinearOpsTensorAlgebra<T> :
     public fun TensorStructure<T>.qr(): Pair<TensorStructure<T>, TensorStructure<T>>
 
     /**
-     * TODO('Andrew')
-     * For more information: https://pytorch.org/docs/stable/generated/torch.lu.html
+     * LUP decomposition
      *
-     * @return ...
-     */
-    public fun TensorStructure<T>.lu(): Pair<TensorStructure<T>, TensorStructure<Int>>
-
-    /**
-     * TODO('Andrew')
-     * For more information: https://pytorch.org/docs/stable/generated/torch.lu_unpack.html
+     * Computes the LUP decomposition of a matrix or a batch of matrices.
+     * Given a tensor `input`, return tensors (P, L, U) satisfying ``P * input = L * U``,
+     * with `P` being a permutation matrix or batch of matrices,
+     * `L` being a lower triangular matrix or batch of matrices,
+     * `U` being an upper triangular matrix or batch of matrices.
      *
-     * @param luTensor ...
-     * @param pivotsTensor ...
-     * @return ...
+     * * @return triple of P, L and U tensors
      */
-    public fun luPivot(luTensor: TensorStructure<T>, pivotsTensor: TensorStructure<Int>):
-            Triple<TensorStructure<T>, TensorStructure<T>, TensorStructure<T>>
+    public fun TensorStructure<T>.lu(): Triple<TensorStructure<T>, TensorStructure<T>, TensorStructure<T>>
 
     /**
      * Singular Value Decomposition.
diff --git a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleLinearOpsTensorAlgebra.kt b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleLinearOpsTensorAlgebra.kt
index 62629f3db..97eed289a 100644
--- a/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleLinearOpsTensorAlgebra.kt
+++ b/kmath-tensors/src/commonMain/kotlin/space/kscience/kmath/tensors/core/algebras/DoubleLinearOpsTensorAlgebra.kt
@@ -29,13 +29,13 @@ public class DoubleLinearOpsTensorAlgebra :
 
     override fun TensorStructure<Double>.det(): DoubleTensor = detLU(1e-9)
 
-    public fun TensorStructure<Double>.lu(epsilon: Double): Pair<DoubleTensor, IntTensor> =
+    public fun TensorStructure<Double>.luFactor(epsilon: Double): Pair<DoubleTensor, IntTensor> =
         computeLU(tensor, epsilon) ?:
         throw RuntimeException("Tensor contains matrices which are singular at precision $epsilon")
 
-    override fun TensorStructure<Double>.lu(): Pair<DoubleTensor, IntTensor> = lu(1e-9)
+    public fun TensorStructure<Double>.luFactor(): Pair<DoubleTensor, IntTensor> = luFactor(1e-9)
 
-    override fun luPivot(
+    public fun luPivot(
         luTensor: TensorStructure<Double>,
         pivotsTensor: TensorStructure<Int>
     ): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
@@ -156,7 +156,7 @@ public class DoubleLinearOpsTensorAlgebra :
     }
 
     public fun TensorStructure<Double>.invLU(epsilon: Double = 1e-9): DoubleTensor {
-        val (luTensor, pivotsTensor) = lu(epsilon)
+        val (luTensor, pivotsTensor) = luFactor(epsilon)
         val invTensor = luTensor.zeroesLike()
 
         val seq = luTensor.matrixSequence().zip(pivotsTensor.vectorSequence()).zip(invTensor.matrixSequence())
@@ -167,6 +167,15 @@ public class DoubleLinearOpsTensorAlgebra :
 
         return invTensor
     }
+
+    public fun TensorStructure<Double>.lu(epsilon: Double = 1e-9): Triple<DoubleTensor, DoubleTensor, DoubleTensor> {
+        val (lu, pivots) = this.luFactor(epsilon)
+        return luPivot(lu, pivots)
+    }
+
+    override fun TensorStructure<Double>.lu(): Triple<DoubleTensor, DoubleTensor, DoubleTensor> = lu(1e-9)
+
+
 }
 
 public inline fun <R> DoubleLinearOpsTensorAlgebra(block: DoubleLinearOpsTensorAlgebra.() -> R): R =
diff --git a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
index 6120f0e4a..1f7e955d4 100644
--- a/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
+++ b/kmath-tensors/src/commonTest/kotlin/space/kscience/kmath/tensors/core/TestDoubleLinearOpsAlgebra.kt
@@ -124,9 +124,7 @@ class TestDoubleLinearOpsTensorAlgebra {
         )
         val tensor = fromArray(shape, buffer)
 
-        val (lu, pivots) = tensor.lu()
-
-        val (p, l, u) = luPivot(lu, pivots)
+        val (p, l, u) = tensor.lu()
 
         assertTrue { p.shape contentEquals shape }
         assertTrue { l.shape contentEquals shape }