# Singular Value Decomposition Calculator

This SVD Calculator, also known as Singular Value Decomposition calculator, is a tool for students and linear algebra learners to calculate the Singular value decomposition values of a matrix.

This calculator give your 3 matrices U, S and V which are used to decompose the input matrix.

## How to use Singular Value Decomposition Calculator

To use the SVD calculator above, follow the steps below:

- enter the number of rows in the first input box
- enter the number of columns in the second input box
- enter the matrix elements in the input boxes provided

Click on the "Calculate" button to get the singular value decomposition of the matrix.

If you find any error in the calculation, please send us the feedback form below the calculator.

## What is Singular Value Decomposition ?

Singular Value Decomposition (SVD) is a process of factorizing the matrix into 3 matrices. The SVD of a matrix A is given by the equation:

\(A = U * S * V^T
\)

where:

- A is a matrix with m rows and n columns
- U is a square matrix with m dimension
- S is a diagonal matrix with m x n dimension
- V is a square matrix with n dimension

## What does U, S and V represent in SVD?

U is a matrix that shows the relationships between the rows of the matrix A.

S is a diagonal matrix that contains the singular values of the matrix A.

V is a matrix that shows the relationships between the columns of the matrix A.

## How to find Singular Value Decomposition ?

To find a SVD of a matrix, you can use the following steps:

## What is Singular Value Decomposition used for?

Singular Value Decomposition is a matrix which retains the most important essence of a matrix. It is used in various fields where the data is to be preserved but size is to be reduced.

For example: Image Compression, Data Compression, Dimensionality Reduction, etc.

## Frequently Asked Questions

### What is the importance of singular value decomposition of a matrix?

The Singular value decomposition of a matrix is important for retaining the information in the matrix while also reducing its size. It is useful for reducing computational complexity by reducing the number of dimensions in the data.