Tool for calculating the minors of a matrix, i.e. the values of the determinants of its square sub-matrices (removing one row and one column of the starting matrix).
Minors of a Matrix - dCode
Tag(s) : Matrix
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Minors of a Matrix
Minors of NxN Matrix Calculator
Answers to Questions (FAQ)
What is a matrix minor? (Definition)
The minors of a square matrix $ M = m_{i, j} $ of size $ n $ are the determinants of the square sub-matrices obtained by removing the row $ i $ and the column $ j $ from $ M $.
Sometimes minors are defined by removing opposing rows and columns (ie. row $ n-i $ and column $ n-j $).
How to calculate a matrix minors?
For a square matrix of order 2, finding the minors is calculating the matrix of cofactors without the coefficients.
For larger matrices like 3x3, calculate the determinants of each sub-matrix.
Example: $$ M = \begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \end{bmatrix} $$
The determinant of the sub-matrix obtained by removing the first row and the first column is: $ ei-fh $$, do the same for all combinations of rows and columns.
What is the difference between a minor and a cofactor?
For a square matrix, the minor is identical to the cofactor except for the sign (indeed, the cofactors can have a - sign depending on their position in the matrix). Minors do not take this minus sign.
Source code
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