Block matrices and Guo’s index for block circulant matrices with circulant blocks

In this paper we deal with circulant and partitioned into n-by-n circulant blocks matrices and introduce spectral results concerning this class of matrices. The problem of fi nding lists of complex numbers corresponding to a set of eigenvalues of a nonnegative block matrix with circulant blocks is treated. Along the paper we call realizable list if its elements are the eigenvalues of a nonnegative matrix. The Guo's index $\lambda_0$ of a realizable list is the minimum spectral radius such that the list (up to the initial spectral radius) together with $\lambda_0$ is realizable. The Guo's index of block circulant matrices with circulant blocks is obtained, and in consequence, necessary and suffcient conditions concerning the NIEP, Nonnegative Inverse Eigenvalue Problem, for the realizability of some spectra are given.publishe

On the spectra of some gg- circulant matrices and applications to nonnegative inverse eigenvalue problem

A $g$-circulant matrix $A$, is defined as a matrix of order $n$ where the elements of each row of $A$ are identical to those of the previous row, but are moved $g$ positions to the right and wrapped around. Using number theory, certain spectra of $g$-circulant real matrices are given explicitly. The obtained results are applied to Nonnegative Inverse Eigenvalue Problem to construct nonnegative, $g$-circulant matrices with given appropriated spectrum. Additionally, some $g$-circulant marices are reconstructed from its main diagonal entries.publishe

Realizable lists via the spectra of structured matrices

A square matrix of order $n$ with $n\geq 2$ is called a \textit{permutative matrix} or permutative when all its rows (up to the first one) are permutations of precisely its first row. In this paper, the spectra of a class of permutative matrices are studied. In particular, spectral results for matrices partitioned into $2$-by-$2$ symmetric blocks are presented and, using these results sufficient conditions on a given list to be the list of eigenvalues of a nonnegative permutative matrix are obtained and the corresponding permutative matrices are constructed. Guo perturbations on given lists are exhibited

Realizable lists on a class of nonnegative matrices

A square matrix of order $n$ with $n\geq 2$ is called \textit{permutative matrix} when all its rows are permutations of the first row. In this paper recalling spectral results for partitioned into $2$-by-$2$ symmetric blocks matrices sufficient conditions on a given complex list to be the list of the eigenvalues of a nonnegative permutative matrix are given. In particular, we study NIEP and PNIEP when some complex elements in the lists under consideration have non-zero imaginary part. Realizability regions for nonnegative permutative matrices are obtained. A Guo's realizability-preserving perturbations result is obtained

Serum human epididymis protein 4 vs. carbohydrate antigen 125 in ovarian cancer follow-up

The addition of human epididymis protein 4 (HE4) to carbohydrate antigen 125 (CA125) in ovarian cancer (OC) assessment has been proposed. We compared the clinical value of biomarker changes in a prospective series of patients undergoing OC monitoring