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 24612a6aa..f234d7d6a 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
@@ -1,5 +1,6 @@
 package space.kscience.kmath.tensors
 
+import space.kscience.kmath.linear.LupDecompositionFeature
 import space.kscience.kmath.nd.MutableNDBuffer
 import space.kscience.kmath.structures.RealBuffer
 import space.kscience.kmath.structures.array
@@ -164,7 +165,19 @@ public class RealTensorAlgebra : TensorPartialDivisionAlgebra<Double, RealTensor
         TODO("Not yet implemented")
     }
 
+    override fun RealTensor.lu(): Pair<RealTensor, RealTensor> {
+        /**
+         * Main first task for @AndreiKingsley
+         * Compare with the implementation of [LupDecomposition]
+         * and provide a common API
+         */
+        TODO("Not yet implemented")
+    }
+
     override fun RealTensor.svd(): Triple<RealTensor, RealTensor, RealTensor> {
+        /**
+         * Main first task for @AlyaNovikova
+         */
         TODO("Not yet implemented")
     }
 
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 cddda7670..03f6f05c2 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
@@ -66,6 +66,9 @@ public interface TensorPartialDivisionAlgebra<T, TensorType : TensorStructure<T>
     public fun TensorType.log(): TensorType
     public fun TensorType.logAssign(): Unit
 
+    //https://pytorch.org/docs/stable/generated/torch.lu.html
+    public fun TensorType.lu(): Pair<TensorType, TensorType>
+
     //https://pytorch.org/docs/stable/generated/torch.svd.html
     public fun TensorType.svd(): Triple<TensorType, TensorType, TensorType>