Invertible matrix

In linear algebra, there are certain matrices which have the property that when they are multiplied with another matrix, the result is the identity matrix $I$ (the matrix with ones on its main diagonal and 0 everywhere). If $A$ is such a matrix, then $A$ is called invertible and its inverse is called $A^{-1}$, with:

$A\cdot A^{-1}=A^{-1}\cdot A=I$

There are algorithms for calculating the inverse of a matrix, with Gaussian elimination being a common example. The problem is that finding the inverse is relatively expensive to do for big matrices. Matrix inversion is used extensively in computer graphics.

Related pages

• Determinant
• Inverse function
• Inverse (mathematics)