Difference between revisions of "Invertible matrix"
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:''AB'' = ''BA'' = I (I: [[identity matrix]]) | :''AB'' = ''BA'' = I (I: [[identity matrix]]) | ||
| − | A matrix is invertible if and only if it has a nonzero determinant. Only square matrices (''n'' x ''n'') are invertible. | + | A matrix is invertible if and only if it has a nonzero [[determinant]]. Only square matrices (''n'' x ''n'') are invertible. |
It can be shown that, for any invertible matrix ''A'', there is only one matrix ''B'' such that ''AB'' = I; this unique matrix is called the [[inverse matrix]] of ''A'', and represented as ''A<sup>-1</sup>''. | It can be shown that, for any invertible matrix ''A'', there is only one matrix ''B'' such that ''AB'' = I; this unique matrix is called the [[inverse matrix]] of ''A'', and represented as ''A<sup>-1</sup>''. | ||
Revision as of 21:36, May 13, 2010
An invertible matrix A is one that has a corresponding matrix B such that:
- AB = BA = I (I: identity matrix)
A matrix is invertible if and only if it has a nonzero determinant. Only square matrices (n x n) are invertible.
It can be shown that, for any invertible matrix A, there is only one matrix B such that AB = I; this unique matrix is called the inverse matrix of A, and represented as A-1.