# LU Decomposition Calculator

An online LU decomposition calculator for decomposing a square matrix into a lower triangular matrix and an upper triangular matrix.

## Calculate Lower, Upper Triangular Matrix Decomposition

An online LU decomposition calculator for decomposing a square matrix into a lower triangular matrix and an upper triangular matrix.

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An **online LU decomposition calculator** which helps you to calculate lower triangular matrix (L) and an upper triangular matrix (U) for the given square matrix using LU Decomposition method.

**LU Decomposition Formula:**
Given here is the formula for decomposing a square matrix. Use this formula and save your time in forming lower triangular and upper triangular matrices out of the given square matrix.

#### Formula:

A = PLU
** Where, **
A = Square Matrix
P = Permutation Matrix
L = Lower Triangular Matrix
U = Upper Triangular Matrix
**LU Decomposition:**
It is also known as LU factorization, introduced by mathematician Tadeusz Banachiewicz in 1938, refers to the factorization of a square matrix A, with proper row and/or column orderings or permutations, into two factors, as lower triangular matrix L and an upper triangular matrix U. 'LU' stands for 'lower upper'. A Triangular matrix is a special kind of square matrix, which can be designated as lower triangular (when all the entries above the main diagonal are zero) and upper triangular (when all the entries below the main diagonal are zero). LU Decompositon of square matrix is applied in numerical analysis and linear algebra. It can be viewed as the matrix form of Gaussian elimination.