Difference between revisions of "Minors and cofactors"
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{{Navigation|before=[[Multiplication of matrices]]|overview=[[Matrices]]|next=[[Determinant of a matrix]]}} | {{Navigation|before=[[Multiplication of matrices]]|overview=[[Matrices]]|next=[[Determinant of a matrix]]}} | ||
− | 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
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