# Minor

*of order *

A determinant of a matrix whose entries are located in a given matrix at the intersection of distinct columns and distinct rows. If the row indices and column indices are the same, then the minor is called principal, and if they are the first rows and columns, then it is called a corner. A basic minor of a matrix is any non-zero minor of maximal order. In order that a non-zero minor be basic it is necessary and sufficient that all minors bordering it (that is, minors of an order higher by one and containing it) are equal to zero. The system of rows (columns) of a matrix related to a basic minor form a maximal linearly independent subsystem of the system of all rows (columns) of the matrix.

#### Comments

Instead of "minor of order k" one also uses "minor of degree k" . Sometimes a minor is not understood to be a determinant (as defined above), but the corresponding submatrix (the notion of "bordering" uses this interpretation).

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Minor.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Minor&oldid=13192