Difference between revisions of "Adjugate Formula"
Line 1: | Line 1: | ||
+ | {{Navigation|before=[[Gauß-Jordan_algorithm]]|overview=[[Matrix inversion|Vektorrechnung]]|next=[[Minors and cofactors]]}} | ||
+ | |||
The adjugate formula defines the inverse of an n-by-n square matrix <math>\mathbf{A}</math> as<br/><br/> | 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})</math><br/><br/> | <math>\mathbf{A}^{-1}=\frac{1}{\det(\mathbf{A})}\text{adj}(\mathbf{A})</math><br/><br/> |
Revision as of 17:05, 9 May 2014
← Back: Gauß-Jordan_algorithm | Overview: Vektorrechnung | Next: Minors and cofactors → |
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
|