Difference between revisions of "Adjugate Formula"
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(Created page with "The adjugate formula defines the inverse of an n-by-n square matrix <math>\mathbf{A}</math> as<br/><br/> <math>\mathbf{A}^{-1}=\frac{1}{\det(\mathbf{A})}\text{adj}(\mathbf{A})...") |
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\text{adj}(\mathbf{A})=\mathbf{C}(\mathbf{A})^T | \text{adj}(\mathbf{A})=\mathbf{C}(\mathbf{A})^T | ||
</math><br/><br/> | </math><br/><br/> | ||
− | And the '''cofactor matrix''' <math>\mathbf{C}(\mathbf{A})</math> is just a matrix where each cell corresponds to the related cofactor:<br/><br/> | + | And the '''cofactor matrix''' <math>\mathbf{C}(\mathbf{A})</math> is just a matrix where each cell corresponds to the related [[Minors_and_cofactors|cofactor]]:<br/><br/> |
<math> | <math> | ||
\mathbf{C}(\mathbf{A})=\left[\begin{array}{cccc} | \mathbf{C}(\mathbf{A})=\left[\begin{array}{cccc} |
Revision as of 15:55, 9 May 2014
The adjugate formula defines the inverse of an n-by-n square matrix as
where is the so called adjugate matrix of . The adjugate matrix is the transposed of the cofactor matrix:
And the cofactor matrix is just a matrix where each cell corresponds to the related cofactor:
So to determine the inverse of an n-by-n square matrix you have to compute the n square cofactors, then transpose the resulting cofactor matrix and divide all the values by the determinant.