Spectral theory of copositive matrices (Q1765921)

An \(n\times n\) real matrix \(A\) is said to be copositive if \(x\geq 0 \rightarrow x^TAx\geq 0\). Copositive matrices in effect have Perron-Frobenius eigenvalues but not generally Perron-Frobenius eigenvectors. The authors prove that for a copositive matrix the eigenvectors corresponding to the nonnegative eigenvalues must however have a linear combination which is positive. For symmetric matrices there is a partial converse. It also gives a block characterization of some copositive matrices.