diff --git a/kmath-noa/src/main/kotlin/space/kscience/kmath/noa/algebras.kt b/kmath-noa/src/main/kotlin/space/kscience/kmath/noa/algebras.kt
index ec91436d6..fbd89a5a4 100644
--- a/kmath-noa/src/main/kotlin/space/kscience/kmath/noa/algebras.kt
+++ b/kmath-noa/src/main/kotlin/space/kscience/kmath/noa/algebras.kt
@@ -252,7 +252,9 @@ protected constructor(scope: NoaScope) :
         JNoa.qrTensor(tensor.tensorHandle, Q, R)
         return Pair(wrap(Q), wrap(R))
     }
-
+    /**
+     * this implementation satisfies `tensor = P dot L dot U`
+     */
     override fun Tensor<T>.lu(): Triple<TensorType, TensorType, TensorType> {
         val P = JNoa.emptyTensor()
         val L = JNoa.emptyTensor()
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 b8a99a560..ad6cc9e78 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
@@ -63,7 +63,7 @@ public interface LinearOpsTensorAlgebra<T> : TensorPartialDivisionAlgebra<T> {
      *
      * Computes the LUP decomposition of a matrix or a batch of matrices.
      * Given a tensor `input`, return tensors (P, L, U) satisfying :
-     * `P dot input = L dot  U` or `input = P dot L dot  U`
+     * `P dot input = L dot U` or `input = P dot L dot U`
      * depending on the implementation, with :
      * `P` being a permutation matrix or batch of matrices,
      * `L` being a lower triangular matrix or batch of matrices,