diff --git a/CHANGELOG.md b/CHANGELOG.md
index aa70e6116..fdf01d4de 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -32,9 +32,10 @@
 - Use `Point<Double>` instead of specialized type in `kmath-for-real`
 - Optimized dot product for buffer matrices moved to `kmath-for-real`
 - EjmlMatrix context is an object
-- Matrix LUP `inverse` renamed to `inverseWithLUP`
+- Matrix LUP `inverse` renamed to `inverseWithLup`
 - `NumericAlgebra` moved outside of regular algebra chain (`Ring` no longer implements it).
 - Features moved to NDStructure and became transparent.
+- Capitalization of LUP in many names changed to Lup.
 
 ### Deprecated
 
diff --git a/examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt b/examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt
index 5ff43ef80..283210174 100644
--- a/examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt
+++ b/examples/src/benchmarks/kotlin/kscience/kmath/benchmarks/LinearAlgebraBenchmark.kt
@@ -26,8 +26,8 @@ class LinearAlgebraBenchmark {
     }
 
     @Benchmark
-    fun kmathLUPInversion() {
-        MatrixContext.real.inverseWithLUP(matrix)
+    fun kmathLupInversion() {
+        MatrixContext.real.inverseWithLup(matrix)
     }
 
     @Benchmark
diff --git a/kmath-core/src/commonMain/kotlin/kscience/kmath/linear/LupDecomposition.kt b/kmath-core/src/commonMain/kotlin/kscience/kmath/linear/LupDecomposition.kt
index 5cf7c8f70..645df429c 100644
--- a/kmath-core/src/commonMain/kotlin/kscience/kmath/linear/LupDecomposition.kt
+++ b/kmath-core/src/commonMain/kotlin/kscience/kmath/linear/LupDecomposition.kt
@@ -151,7 +151,7 @@ public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext
 public fun MatrixContext<Double, Matrix<Double>>.lup(matrix: Matrix<Double>): LupDecomposition<Double> =
     lup(Buffer.Companion::real, RealField, matrix) { it < 1e-11 }
 
-public fun <T : Any> LupDecomposition<T>.solveWithLUP(
+public fun <T : Any> LupDecomposition<T>.solveWithLup(
     factory: MutableBufferFactory<T>,
     matrix: Matrix<T>,
 ): Matrix<T> {
@@ -199,14 +199,14 @@ public fun <T : Any> LupDecomposition<T>.solveWithLUP(
     }
 }
 
-public inline fun <reified T : Any> LupDecomposition<T>.solveWithLUP(matrix: Matrix<T>): Matrix<T> =
-    solveWithLUP(MutableBuffer.Companion::auto, matrix)
+public inline fun <reified T : Any> LupDecomposition<T>.solveWithLup(matrix: Matrix<T>): Matrix<T> =
+    solveWithLup(MutableBuffer.Companion::auto, matrix)
 
 /**
- * Solve a linear equation **a*x = b** using LUP decomposition
+ * Solves a system of linear equations *ax = b** using LUP decomposition.
  */
 @OptIn(UnstableKMathAPI::class)
-public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.solveWithLUP(
+public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.solveWithLup(
     a: Matrix<T>,
     b: Matrix<T>,
     noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
@@ -214,26 +214,26 @@ public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext
 ): Matrix<T> {
     // Use existing decomposition if it is provided by matrix
     val decomposition = a.getFeature() ?: lup(bufferFactory, elementContext, a, checkSingular)
-    return decomposition.solveWithLUP(bufferFactory, b)
+    return decomposition.solveWithLup(bufferFactory, b)
 }
 
-public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.inverseWithLUP(
+public inline fun <reified T : Comparable<T>, F : Field<T>> GenericMatrixContext<T, F, Matrix<T>>.inverseWithLup(
     matrix: Matrix<T>,
     noinline bufferFactory: MutableBufferFactory<T> = MutableBuffer.Companion::auto,
     noinline checkSingular: (T) -> Boolean,
-): Matrix<T> = solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
+): Matrix<T> = solveWithLup(matrix, one(matrix.rowNum, matrix.colNum), bufferFactory, checkSingular)
 
 
 @OptIn(UnstableKMathAPI::class)
-public fun RealMatrixContext.solveWithLUP(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
+public fun RealMatrixContext.solveWithLup(a: Matrix<Double>, b: Matrix<Double>): Matrix<Double> {
     // Use existing decomposition if it is provided by matrix
     val bufferFactory: MutableBufferFactory<Double> = MutableBuffer.Companion::real
     val decomposition: LupDecomposition<Double> = a.getFeature() ?: lup(bufferFactory, RealField, a) { it < 1e-11 }
-    return decomposition.solveWithLUP(bufferFactory, b)
+    return decomposition.solveWithLup(bufferFactory, b)
 }
 
 /**
  * Inverses a square matrix using LUP decomposition. Non square matrix will throw a error.
  */
-public fun RealMatrixContext.inverseWithLUP(matrix: Matrix<Double>): Matrix<Double> =
-    solveWithLUP(matrix, one(matrix.rowNum, matrix.colNum))
\ No newline at end of file
+public fun RealMatrixContext.inverseWithLup(matrix: Matrix<Double>): Matrix<Double> =
+    solveWithLup(matrix, one(matrix.rowNum, matrix.colNum))
\ No newline at end of file
diff --git a/kmath-core/src/commonTest/kotlin/kscience/kmath/linear/RealLUSolverTest.kt b/kmath-core/src/commonTest/kotlin/kscience/kmath/linear/RealLUSolverTest.kt
index 28dfe46ec..d2822a221 100644
--- a/kmath-core/src/commonTest/kotlin/kscience/kmath/linear/RealLUSolverTest.kt
+++ b/kmath-core/src/commonTest/kotlin/kscience/kmath/linear/RealLUSolverTest.kt
@@ -9,7 +9,7 @@ class RealLUSolverTest {
     @Test
     fun testInvertOne() {
         val matrix = MatrixContext.real.one(2, 2)
-        val inverted = MatrixContext.real.inverseWithLUP(matrix)
+        val inverted = MatrixContext.real.inverseWithLup(matrix)
         assertEquals(matrix, inverted)
     }
 
@@ -37,7 +37,7 @@ class RealLUSolverTest {
             1.0, 3.0
         )
 
-        val inverted = MatrixContext.real.inverseWithLUP(matrix)
+        val inverted = MatrixContext.real.inverseWithLup(matrix)
 
         val expected = Matrix.square(
             0.375, -0.125,
diff --git a/kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealMatrix.kt b/kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealMatrix.kt
index 274030aff..69e211624 100644
--- a/kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealMatrix.kt
+++ b/kmath-for-real/src/commonMain/kotlin/kscience/kmath/real/RealMatrix.kt
@@ -2,7 +2,7 @@ package kscience.kmath.real
 
 import kscience.kmath.linear.MatrixContext
 import kscience.kmath.linear.VirtualMatrix
-import kscience.kmath.linear.inverseWithLUP
+import kscience.kmath.linear.inverseWithLup
 import kscience.kmath.linear.real
 import kscience.kmath.misc.UnstableKMathAPI
 import kscience.kmath.structures.Buffer
@@ -152,7 +152,7 @@ public inline fun RealMatrix.map(transform: (Double) -> Double): RealMatrix =
 /**
  * Inverse a square real matrix using LUP decomposition
  */
-public fun RealMatrix.inverseWithLUP(): RealMatrix = MatrixContext.real.inverseWithLUP(this)
+public fun RealMatrix.inverseWithLup(): RealMatrix = MatrixContext.real.inverseWithLup(this)
 
 //extended operations