arXiv subjects
Publications and source records attributed to Thomas J. Laffey.
We show that if a list of nonzero complex numbers $σ=(λ_1,λ_2,\ldots,λ_k)$ is the nonzero spectrum of a diagonalizable nonnegative matrix, then $σ$ is the nonzero spectrum of a diagonalizable nonnegative matrix of order $k+k^2.$
In the first two sections of this paper we provide a brief account of the Cayley-Dickson algebras and prove that the radius on these algebras is given by the Euclidean norm. With this observation we resort to three related topics: a variant of the Gelfand formula, stability of subnorms, and the functional power equation.
Let A be an nxn (entrywise) positive matrix and let f(t)=det(I-t A). We prove that there always exists a positive integer N such that 1-f(t)^{1/N} has positive coefficients.
A constructive version of the celebrated Boyle-Handelman theorem on the non-zero spectra of nonnegative matrices is presented.