Definition

The derivatives of a given submatrix of matrix .

Example

1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9\\ \end{array}\right]$$ Has principal minors:

\det \left[\begin{array}{cc} 1 \end{array}\right]

\det \left[\begin{array}{cc} 1 & 2\ 4 & 5\ \end{array}\right]

\det \left[\begin{array}{cc} 1 & 2 & 3\ 4 & 5 & 6\ 7 & 8 & 9\ \end{array}\right]