Zero sum sign-central matrices and applications

Abstract

A matrix with a nonzero nonnegative vector in its null space is called central . We study classes of central matrices having zero column sums. The study is motivated by an engineering application concerning induction heating where central matrices provide a way to control the energy flow over time. A (±1)(±1)-matrix A is called a ZSC-matrix (zero sum sign-central) if each matrix with the same sign pattern as A and having zero column sums is central. We establish several classes of ZSC-matrices, and give separate sufficient and necessary conditions for a matrix to be ZSC. Moreover, we give algorithms for finding central matrices that are used for power control in induction heating, and illustrate these by some numerical examples.