Difference between revisions of "Minors and cofactors"
From Robotics
Line 73: | Line 73: | ||
0&0&1 | 0&0&1 | ||
\end{array}\right|=-1-0=-1 | \end{array}\right|=-1-0=-1 | ||
− | + | </math> | |
− | <math>M_{42}(^R\mathbf{T}_N)= | + | :<math> |
+ | M_{42}(^R\mathbf{T}_N)= | ||
\left|\begin{array}{cccc} | \left|\begin{array}{cccc} | ||
0&\Box&0&2a\\ | 0&\Box&0&2a\\ | ||
0&\Box&-1&0\\ | 0&\Box&-1&0\\ | ||
− | -1&\Box&0&0 | + | -1&\Box&0&0\\ |
\Box & \Box & \Box & \Box\\ | \Box & \Box & \Box & \Box\\ | ||
\end{array}\right|= | \end{array}\right|= |
Revision as of 16:10, 22 May 2014
← Back: Determinant of a matrix | Overview: Matrices | Next: Matrix inversion → |
The minor of an n-by-n square matrix is the determinant of a smaller square matrix obtained by removing the row and the column from .
Multiplying the minor with results in the cofactor :
Example: Minors and cofactors of a 3-by-3 matrix
The minors and for example are defined as The corresponding cofactors in that case are |
Example: Minors and cofactors of a 4-by-4 matrix
This example uses the transformation matrix that is introduced in the robotics script in chapter 3 on page 3-37 and used on the following pages.
The minors and for example are defined as
|