The fibre of P-matrices: the recursive construction of all matrices with positive principal minors
Michael J. Tsatsomeros, Yueqiao Faith Zhang · Linear and Multilinear Algebra · 2019
P-matrices have positive principal minors and include many well-known matrix classes (positive definite, totally positive, M-matrices, etc.) How does one construct a generic P-matrix? Specifically, is there a characterization of P-matrices that lends itself to the tractable construction of every P-matrix? To answer these questions positively, a recursive method is employed that is based on a characterization of rank-one perturbations that preserve the class of P-matrices.