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}=I_{n}. The identity matrix is
identified by the symbol I_{n}, 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.