diff --git a/lax/src/lib.rs b/lax/src/lib.rs
index d8d2d831..d7b1be4a 100644
--- a/lax/src/lib.rs
+++ b/lax/src/lib.rs
@@ -4,7 +4,7 @@
 //! -------------------------------
 //!
 //! This crates provides LAPACK wrapper as `impl` of traits to base scalar types.
-//! For example, LU factorization to double-precision matrix is provided like:
+//! For example, LU decomposition to double-precision matrix is provided like:
 //!
 //! ```ignore
 //! impl Solve_ for f64 {
@@ -46,7 +46,7 @@
 //! Linear equation, Inverse matrix, Condition number
 //! --------------------------------------------------
 //!
-//! According to the property input metrix, several types of triangular factorization are used:
+//! According to the property input metrix, several types of triangular decomposition are used:
 //!
 //! - [Solve_] trait provides methods for LU-decomposition for general matrix.
 //! - [Solveh_] triat provides methods for Bunch-Kaufman diagonal pivoting method for symmetric/hermite indefinite matrix.
diff --git a/lax/src/solve.rs b/lax/src/solve.rs
index 565aab59..9f25c9bf 100644
--- a/lax/src/solve.rs
+++ b/lax/src/solve.rs
@@ -5,7 +5,7 @@ use num_traits::{ToPrimitive, Zero};
 #[cfg_attr(doc, katexit::katexit)]
 /// Solve linear equations using LU-decomposition
 ///
-/// For a given matrix $A$, LU decomposition is described as $PA = LU$ where
+/// For a given matrix $A$, LU decomposition is described as $A = PLU$ where:
 ///
 /// - $L$ is lower matrix
 /// - $U$ is upper matrix
@@ -15,15 +15,15 @@ use num_traits::{ToPrimitive, Zero};
 ///
 /// 1. Factorize input matrix $A$ into $L$, $U$, and $P$.
 /// 2. Solve linear equation $Ax = b$ or compute inverse matrix $A^{-1}$
-///    using the output of LU factorization.
+///    using the output of LU decomposition.
 ///
 pub trait Solve_: Scalar + Sized {
-    /// Computes the LU factorization of a general $m \times n$ matrix
+    /// Computes the LU decomposition of a general $m \times n$ matrix
     /// with partial pivoting with row interchanges.
     ///
     /// Output
     /// -------
-    /// - $U$ and $L$ are stored in `a` after LU factorization has succeeded.
+    /// - $U$ and $L$ are stored in `a` after LU decomposition has succeeded.
     /// - $P$ is returned as [Pivot]
     ///
     /// Error