Difference between revisions of "Minors and cofactors"
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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 :