Abstract. We consider a list of complex numbers Λ = {λ 1 , λ 2 , . . . , λn} and give a simple and efficient sufficient condition for the existence of an n × n nonnegative matrix with spectrum Λ. Our result extends a previous one for a list of real numbers given in [Linear Algebra Appl., 416: [844][845][846][847][848][849][850][851][852][853][854][855][856] 2006]. In particular, we show how to construct a nonnegative matrix with prescribed complex eigenvalues and diagonal entries. As a by-product, we also construct Hermitian matrices with prescribed spectrum, whose entries have nonnegative real parts.

We consider the following inverse eigenvalue problem: to construct a symmetrical tridiagonal matrix from the minimal and maximal eigenvalues of all its leading principal submatrices. We give a necessary and sufficient condition for the existence of such a matrix and for the existence of a nonnegative symmetrical tridiagonal matrix. Our results are constructive, in the sense that they generate an algorithmic procedure to construct the matrix.

No abstract

No abstract

We consider the problem of constructing positive matrices with prescribed singular values. In particular, we show how to construct an m × n positive matrix, m ≥ n, with prescribed singular values σ 1 ≤ σ 2 ≤ • • • ≤ σ n .