On \(P\)-matrices (Q1870055)

A real matrix \(A\in M_n(R)\) is called a \(P\)-matrix if all its principal minors are positive. In this paper the author considers the \(P\)-problem, namely the problem of checking whether a given matrix is a \(P\)-matrix. In Sections 2 and 3, he investigates some necessary and sufficient conditions for a real matrix to be a \(P\)-matrix, basing on the sign real spectral radius and regularity of a certain interval matrix. Finally, in Section 4 he presents a not necessarily exponential method for checking the \(P\)-property, by giving an algorithm and many illustrative numerical examples.