2021/06/16 by Wu, Chengshuai, Margaliot, Michael
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2106.08656
A matrix is called a P-matrix if all its principal minors are positive. P-matrices have found important applications in functional analysis, mathematical programming, and dynamical systems theory. We introduce a new class of real matrices denoted~\EP. A matrix is in~\EP if and only if its matrix exponential is a P-matrix for all positive times. In other words, A∈ \EP if and only if the transition matrix of the linear system~ x=Ax is a P-matrix for any positive time~t. We analyze the properties of this new class of matrices and describe an application of our theoretical results to opinion dynamics.