In mathematics, a P-matrix is a complex square matrix with every principal minor is positive.
-matrices, which are the closure of the class of P-matrices, with every principal minor
By a theorem of Kellogg,[1][2] the eigenvalues of P- and
- matrices are bounded away from a wedge about the negative real axis as follows: The class of nonsingular M-matrices is a subset of the class of P-matrices.
More precisely, all matrices that are both P-matrices and Z-matrices are nonsingular M-matrices.
The class of sufficient matrices is another generalization of P-matrices.
has a unique solution for every vector q if and only if M is a P-matrix.
[5] A related class of interest, particularly with reference to stability, is that of
, the eigenvalues of these matrices are bounded away from the positive real axis.