Difference between revisions of "Adjugate Formula"
From Robotics
Line 20: | Line 20: | ||
|Contents= | |Contents= | ||
<br/><math> | <br/><math> | ||
− | \mathbf{A}_e | + | \mathbf{A}_e = |
\left[\begin{array}{cccc} | \left[\begin{array}{cccc} | ||
1 & 2 & 0 & 0\\ | 1 & 2 & 0 & 0\\ | ||
Line 28: | Line 28: | ||
\end{array}\right]</math> | \end{array}\right]</math> | ||
<br/><br/> | <br/><br/> | ||
− | The calculation of two of the cofactors of <math>\mathbf{A}_e</math> has already been described in the example for [[Minors_and_cofactors|minors and cofactors]] and the determinant is computed [[Determinant_of_a_4-by-4_matrix|here]]. | + | The calculation of two of the cofactors of <math>\mathbf{A}_e</math> has already been described in the example for [[Minors_and_cofactors|minors and cofactors]] and the determinant is computed [[Determinant_of_a_4-by-4_matrix|here]].<br/><br/> |
<math>\begin{align} | <math>\begin{align} | ||
\mathbf{C}(\mathbf{A}_e)&= | \mathbf{C}(\mathbf{A}_e)&= |
Revision as of 16:06, 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.
Example: inverse of a 4-by-4 matrix
|