Difference between revisions of "Adjugate Formula"
Line 67: | Line 67: | ||
\end{array}\right] | \end{array}\right] | ||
</math> | </math> | ||
+ | }} | ||
− | + | [[Category:Article]] | |
+ | [[Category:Matrices]] |
Revision as of 10:54, 12 May 2014
← Back: Gauß-Jordan-Algorithm | Overview: Matrix inversion | Next: Matrix Inversion → |
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.
Example: inverse of a 4-by-4 matrix using the adjugate formula
|