Difference between revisions of "Minors and cofactors"
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| − | The '''minor <math>M_{i,j}(\mathbf{A})</math>''' of an n-by-n square matrix <math>\mathbf{A}</math> is the determinant of a smaller square matrix obtained by removing the row <math>i</math> and the column <math>j</math> from <math>\mathbf{A}</math>.<br/><br/> | + | The '''minor <math>M_{i,j}(\mathbf{A})</math>''' of an n-by-n square matrix <math>\mathbf{A}</math> is the [[Determinant of a matrix|determinant]] of a smaller square matrix obtained by removing the row <math>i</math> and the column <math>j</math> from <math>\mathbf{A}</math>.<br/><br/> |
Multiplying the minor with <math>(-1)^{i+j}</math> results in the '''cofactor <math>C_{i,j}(\mathbf{A})</math>''':<br/><br/> | Multiplying the minor with <math>(-1)^{i+j}</math> results in the '''cofactor <math>C_{i,j}(\mathbf{A})</math>''':<br/><br/> | ||
Revision as of 15:46, 22 May 2014
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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
|
![\mathbf{A}_e =
\left[\begin{array}{cccc}
1 & 2 & 0 & 0\\
3 & 0 & 1 & 1\\
0 & 1 & 0 & 0\\
0 & 0 & 2 & 1
\end{array}\right]](/wiki/robotics/images/math/a/3/8/a386cb4eac26aca26ac89fd336061a0e.png)
and 
for example are defined as
