Difference between revisions of "Invertible matrix"
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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. | ||
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| + | 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>''. | ||
[[Category:linear algebra]] | [[Category:linear algebra]] | ||
[[Category:mathematics]] | [[Category:mathematics]] | ||
Revision as of 18:08, 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.