 # LU Decomposition

Matrix A
row
column

## What is LU Decomposition Calculator with Steps?

LU matrix decomposition calculator is an online matrix calculator that is used to factorize a square of any order into two distinct triangular matrices. These triangle matrices form individually one lower triangle matrix (L) and one upper triangle matrix (U).

This lu decomposition method calculator offered by matrix solver calculator uses the LU decomposition method in order to convert a square matrix to upper and lower triangle matrices. The decomposition formula used by this lu calculator states,

A = PLU

Related:You can also calculate matrices through gauss jordan elimination method by using our augmented matrix calculator for free.

Remembering the formula above which is A = PLU.. So the square matrix in the formula is given as A, while the P represents the Permutation Matrix. The LU decomposition also known as LU factorization is considered as the matrix form Gaussian Elimination. And we know that this can be messy, and to solve this mess we introduce you the lu matrix calculator online for free.

This lu matrix decomposition calculator is an effective tool for linear algebraic problem-solving. As linear algebraic operations and numerical analysis is involved in the LU decomposition performed on the square matrix to factorize into triangle matrices.

## How to Use LU Decomposition Calculator Step by Step?

The lu matrix calculator is available online to decompose any square matrice to lower and upper triangle matrices. All you need to use is this helpful matrix decomposition calculator in your portable device and an internet connection enabled on it.

Using this lu factorization calculator with steps decomposing matrices into their triangle matrix components is a two-step procedure , i.e. give inputs and get results. However, the following steps will help you guide, how to use the matrix calculator for LU decomposition.

Related:You can also take determinant of the matrix through determinant of 4x4 matrix calculator but can calculate for the 6x6 also. And can can also take inverse of the matrix through inverse matrix calculator with steps easily.

## Select LU Decomposition Solver

From the website of matrix calculator providing extensive tools for matrix operations and calculations, select the matrix lu decomposition calculator first of all. You will be redirected to the matrix decomposition calculator where you have to input your square matrix to get triangle matrices.

### Enter Matrix Dimensions

In the lu decomposition calculator with steps start giving inputs of your square matrix. As the first input enter the size of your matrix i.e. mxn. The dimension of a square could be selected up to 6x6 in this lu calculator.

### Input Matrix Values

Now, enter the values of your matrix as its elements in the decomposition lu calculator, While entering the elements be sure to input correct values.

### Get Results

As the last step, get your results of LU decomposition. Simply click on the calculate button and you will be provided with the final results as two lower and upper triangle matrices.

Related: As you know trace of a matrix is equal to the sum of eigen values. You can calculate trace of matrix and also use eigenvalue finder from this matrix calculator.

## FAQs

### How to solve LU Decomposition?

The LU decomposition or factorization involves converting the square matrix into two triangular matrices. The formula is A = PLU. Where A is the square matrix and P is the permutation of matrix.The manuall way can be lengthy but you can solve easily through lu factorization calculator online.

### What is P in LU decomposition?

P is the Permutation matrix. This permutation matrix is calculated in the case of partial pivoting. As sometimes solving linear equations using lu factorization calculator, it also gives another matrix, which is Permutation matrix in the results.

### Does LU Decomposition always exist?

LU Decomposition of any linear system is always exists as it helps to find out the determinant of a matrix. If the determinant of a matrix is not 0, then pure LU decomposition exists only if principal minors are not 0.

Thus we can easily check decomposition exists or not by using lu decomposition online calculator within a second.

We hope you enjoyed our matrix lu factorization calculator. You can also use other matrices tools available. such as to find eigenvalues of matrix calculator and matrix difference calculator for free.

By James Johnson - Last Updated January 24, 2022