Principal minor

A principal minor is the determinant of a square submatrix selected using the same index set for rows and columns. For a three-by-three matrix, the coefficient of $\lambda$ in its monic characteristic polynomial is the sum of its three principal minors of order two.

A leading principal minor is a principal minor using the first $k$ rows and columns of a square matrix in a specified ordering. Sylvester's criterion uses these minors to characterize positive-definite matrices.