An improved bound for a fundamental constant associated with a P-matrix
Roy Mathias · Applied Mathematics Letters · 1989
Let M be an n -by- n P-matrix. We determine the optimal lower bound for the quantity α(M) ≡ min { max i x i (Mx) i : x ϵ R n , ‖x‖ ∞ = 1} based on the real eigenvalues of the principal submatrices of M and the maximum of the absolute values of the off-diagonal entries of M . This bound is positive whenever M is a P-matrix.