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><br/><br/> |
:<math> | :<math> | ||
M_{42}(^R\mathbf{T}_N)= | M_{42}(^R\mathbf{T}_N)= | ||
Line 90: | Line 90: | ||
<br/><br/> | <br/><br/> | ||
The corresponding cofactors in that case are<br/><br/> | The corresponding cofactors in that case are<br/><br/> | ||
− | :<math>C_{ | + | :<math>C_{31}(^R\mathbf{T}_N)=(-1)^{3+1}M_{31}(^R\mathbf{T}_N)=(-1)^4\cdot(-1)=-1</math> |
− | :<math>C_{ | + | :<math>C_{42}(^R\mathbf{T}_N)=(-1)^{4+2}M_{42}(^R\mathbf{T}_N)=(-1)^6\cdot(-2a)=-2a</math> |
}} | }} | ||
[[Category:Article]] | [[Category:Article]] | ||
[[Category:Matrices]] | [[Category:Matrices]] |
Revision as of 16:12, 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
|