Matrix inverse: Difference between revisions
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imported>Richard Pinch ("invertible" is an anchor; inverse is unique) |
imported>Richard Pinch m (link) |
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The '''inverse''' of a square [[matrix(mathematics)|matrix]] '''A''' is '''X''' if | The '''inverse''' of a square [[matrix (mathematics)|matrix]] '''A''' is '''X''' if | ||
:<math>\mathbf{AX} = \mathbf{XA} = \mathbf{I}_n \ </math> | :<math>\mathbf{AX} = \mathbf{XA} = \mathbf{I}_n \ </math> | ||
Revision as of 01:07, 10 December 2008
The inverse of a square matrix A is X if
(In is the n-by-n identity matrix). If this equation is true, X is the inverse of A, denoted by A-1 ( and A is the inverse of X). Furthermore, the inverse X is unique (if Y were also an inverse consider X.A.Y).
A matrix is invertible if and only if it possesses an inverse. A matrix is invertible if and only if its determinant is itelf invertible: over a field such as the real or complex numbers, this is equivalent to specifying that the determinant does not equal zero.