Matrix inverse: Difference between revisions
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imported>Todd Coles No edit summary |
imported>Richard Pinch (comment to take care of determinant over a ring) |
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('''I'''<sub>''n''</sub> is the ''n''-by-''n'' [[identity matrix]]). If this equation is true, '''X''' is the inverse of '''A''', denoted by '''A'''<sup>-1</sup> ( and '''A''' is the inverse of '''X'''). | ('''I'''<sub>''n''</sub> is the ''n''-by-''n'' [[identity matrix]]). If this equation is true, '''X''' is the inverse of '''A''', denoted by '''A'''<sup>-1</sup> ( and '''A''' is the inverse of '''X'''). | ||
A matrix is ''invertible'' if and only if its [[determinant]] does not equal zero. | A matrix is ''invertible'' if and only if its [[determinant]] is itelf invertible: over a [[field (mathematics)|field]] such as the [[real number|real]] or [[complex number]]s, this is equivalent to specifying that the determinant does not equal zero. | ||
Revision as of 01:03, 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).
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.