# P-matrix

A square matrix with all of its principal minors positive. This includes all symmetric, positive definite matrices. Here is an example of a P-matrix that is not positive definite:

$LaTeX: A = \begin{bmatrix} 1 & -3 \\ 0 & 1 \end{bmatrix}$

The principal minors are positive, but $LaTeX: \textstyle (1, 1)A(1, 1)^t < 0.$ The significance of this class is in the theorem:

The linear complementarity problem, defined by $LaTeX: (M, q),$ has a unique solution for each q in Rn if, and only if, $LaTeX: M$ is a P-matrix.