Difference between revisions of "Minors and cofactors"
From Robotics
Line 3: | Line 3: | ||
The '''minor <math>M_{ij}(\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/> | The '''minor <math>M_{ij}(\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_{ | + | Multiplying the minor with <math>(-1)^{i+j}</math> results in the '''cofactor <math>C_{ij}(\mathbf{A})</math>''':<br/><br/> |
<math>C_{i,j}(\mathbf{A})=(-1)^{i+j}M_{ij}(\mathbf{A})</math><br/><br/> | <math>C_{i,j}(\mathbf{A})=(-1)^{i+j}M_{ij}(\mathbf{A})</math><br/><br/> | ||
Revision as of 16:13, 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
:
![]()
The minors The corresponding cofactors in that case are |
![]() This example uses the transformation matrix The minors
|