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 [math]\displaystyle{ I }[/math] (the matrix with ones on its main diagonal and 0 everywhere). If [math]\displaystyle{ A }[/math] is such a matrix, then [math]\displaystyle{ A }[/math] is called invertible and its inverse is called [math]\displaystyle{ A^{-1} }[/math], with:

[math]\displaystyle{ A \cdot A^{-1} = A^{-1} \cdot A = I }[/math]

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)