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Young-type inequalities and their matrix analogues
We present several new Young-type inequalities for positive real numbers and we apply our results to obtain the matrix analogues. Among others, for real numbers , and , with and , we prove theExpand
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The singular acyclic matrices with the second largest number of P-vertices
Suppose that the nullity of the submatrix obtained from the deletion of a row and a column of the same index of a real symmetric matrix goes up by one. Such an index is called a P-vertex of the givenExpand
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Vertex types in some lexicographic products of graphs
ABSTRACT Let be a symmetric matrix, or equivalently, a weighted graph whose edge ij has the weight . The eigenvalues of are the eigenvalues of M. We denote by the principal submatrix of M obtained byExpand
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A matrix approach to some second-order difference equations with sign-alternating coefficients
ABSTRACT In this paper, we analyse and unify some recent results on the double sequence , for , defined by the second-order difference equation with and , in terms of matrix theory and orthogonalExpand
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The μ-permanent revisited
This letter aims to correct and clarify several results appearing in [2]. It is clear that, under similarity, the -permanent does not keep the same value, in general, i.e. the polynomial P (A) is notExpand
Comment on "Thermal transport in dimerized harmonic lattices: Exact solution, crossover behavior, and extended reservoirs".
In this Comment we recall the notion of a tridiagonal 2-Toeplitz matrix and its spectrum, confronting these results with others obtained recently on exact solutions of thermal transport in dimerizedExpand
A new type of Sylvester–Kac matrix and its spectrum
ABSTRACT The Sylvester–Kac matrix, sometimes known as Clement matrix, has many extensions and applications throughout more than a century of its existence. The computation of the eigenvalues or evenExpand
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A Short Note on the Determinant of a Sylvester–Kac Type Matrix
Abstract The Sylvester–Kac matrix, also known as Clement matrix, has many extensions and applications. The evaluation of determinant and spectra of many of its generalizations sometimes are hard toExpand
On a conjecture about a tridiagonal matrix
Abstract In this note we answer to a recent conjecture posed by Q.M. Al-Hassan on a factorization for the characteristic polynomial of the tridiagonal matrix with zero main diagonal and all 1’s sub-Expand
Tridiagonal Matrices and Spectral Properties of Some Graph Classes
A graph is called a chain graph if it is bipartite and the neighbourhoods of the vertices in each colour class form a chain with respect to inclusion. In this paper we give an explicit formula forExpand