Minors and cofactors
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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 Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): M_{42}(^R\mathbf{T}_N)= \left|\begin{array}{cccc} 0&\Box&0&2a\\ 0&\Box&-1&0\\ -1&\Box&0&0 \Box & \Box & \Box & \Box\\ \end{array}\right|= \left|\begin{array}{ccc} 0&0&2a\\ 0&-1&0\\ -1&0&0 \end{array}\right|=0-2a=-2a
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