Difference between revisions of "Minors and cofactors"
From Robotics
m (Nickchen moved page Minors and-cofactors to 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 smaller square matrix obtained by removing the row <math>i</math> and the column <math>j</math> from <math>\mathbf{A}</math>.<br/><br/> | ||
| − | + | {{Example | |
| − | + | |Title=Minors | |
| + | |||
| + | The minors <math>M_{1,4}(\mathbf{A}_e)</math> and <math>M_{3,1}(\mathbf{A}_e)</math> for example are defined as<br/><br/> | ||
| + | <math>M_{1,4}(\mathbf{A}_e)= | ||
\left|\begin{array}{cccc} | \left|\begin{array}{cccc} | ||
\Box & \Box & \Box & \Box\\ | \Box & \Box & \Box & \Box\\ | ||
Revision as of 15:34, 9 May 2014
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 .
{{Example |Title=Minors
The minors 
and 
for example are defined as
Multiplying the minor with 
results in the cofactor 
:
