Abstract
A real matrix A is said to be an M-matrix if it is of the form where B is a nonnegative matrix with Perron eigenvalue and . This paper provides sufficient conditions for the existence and construction of an M-matrix A with prescribed elementary divisors, which are the characteristic polynomials of the Jordan blocks of the Jordan canonical form of A. This inverse problem on M-matrices has not been treated until now. We solve the inverse elementary divisors problem for diagonalizable M-matrices and the symmetric generalized doubly stochastic inverse M-matrix problem for lists of real numbers and for lists of complex numbers of the form . The constructive nature of our results allows for the computation of a solution matrix. The paper also discusses an application of M-matrices to a capacity problem in wireless communications.
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