• # Matrix Inversion

In algebra, the inverse of a number n is 1/n which is also called the reciprocal of the number n. This can also be written as n-1. In the case of matrices, for a square matrix such as A, Fig to the far right, the inverse can only be written as A-1, as division in matrices does not exit. Non-square matrices do not have inverse.
In the case of numbers, when a number n is multiplied by its reciprocal n-1, the result is 1. Similarly when the matrix A is multiplied by its inverse A-1, the result is known as the identity or unit matrix, i.e. A*A-1=In. The identity matrix is identified by the symbol In, with 1s on the main diagonal and 0s elsewhere.
Note: Not all square matrices have inverse. Square matrices which have inverse are called invertible, nonsingular or nonedegenerate. Square matrices which have no inverse are called noninvertible, singular or degenerate.
There are several methods by which a matrix can be inverted, these method are explained in depth in Wikipedia, as well as other specialized sites. Some of these methods are listed to the right.

Use the following tool to find the inverse of a square matrix.

## Inversion Methods

 Methods of Matrix Inversion Guassian Eleminiation Newton's method Cayley-Hamilton Eigendecomposition of a Matix Cholesky decomposition

## Matrix Inversion Tool

This program allows the user to invert a square matrix.

#### How to use the program:

Enter the dimension n of a square matrix, click on Create Matrix Grid button. This will create a square grid n*n, for the square matrix elements to be entered. Once all elements are entered, click on Invert Matrix button. The inverted matrix will appear under the entered matrix.

Size n =