P-matrix

In mathematics, a -matrix is a complex square matrix with every principal minor is positive. A closely related class is that of P_0-matrices, which are the closure of the class of -matrices, with every principal minor \geq 0.

== Spectra of -matrices == By a theorem of Kellogg, the eigenvalues of - and P_0- matrices are bounded away from a wedge about the negative real axis as follows: If \{u_1,...,u_n\} are the eigenvalues of an -dimensional -matrix, where n>1, then |\arg(u_i)| If \{u_1,...,u_n\}, u_i \neq 0, i = 1,...,n are the eigenvalues of an -dimensional P_0-matrix, then |\arg(u_i)| \leq \pi - \frac{\pi}{n},\ i = 1,...,n