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Minors of a Matrix

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).

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Minors of a Matrix -

Tag(s) : Matrix

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Minors of a Matrix

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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.

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