Matrix Minor

A matrix minor is the determinant of a submatrix obtained by deleting one or more rows and/or columns from a given matrix. Specifically:

$k$-th Order Minor

In an $n$-by-$n$ matrix, a $k$-th order minor is the determinant of a $k$-by-$k$ submatrix, where $k$ can be any integer between $1$ and $n$. The $k$ rows and $k$ columns can be any combination, as long as the number of rows and columns are equal.

Principal Minor

A principal minor is a minor where the rows and columns selected have the same row/column indices. For example, selecting the $i_1$th, $i_2$th, ..., $i_k$th rows and columns.

Leading Principal Minor

A leading principal minor is a principal minor where the selected rows and columns have consecutive indices, i.e. the first $k$ rows and columns. The $k$-th leading principal minor of a given matrix is unique