A relative Laplacian spectral recursion.
A remark on the eigenvalues of generalized circulants
A result related to the largest eigenvalue of a tree
In this note we prove that {0,1,√2,√3,2} is the set of all real numbers l such that the following holds: every tree having an eigenvalue which is larger than l has a subtree whose largest eigenvalue is l.
A robust spectral method for finding lumpings and meta stable states of non-reversible Markov chains.
A sharp upper bound for the spectral radius of a nonnegative matrix and applications
We obtain a sharp upper bound for the spectral radius of a nonnegative matrix. This result is used to present upper bounds for the adjacency spectral radius, the Laplacian spectral radius, the signless Laplacian spectral radius, the distance spectral radius, the distance Laplacian spectral radius, the distance signless Laplacian spectral radius of an undirected graph or a digraph. These results are new or generalize some known results.
A shorter proof of the distance energy of complete multipartite graphs
Caporossi, Chasser and Furtula in [Les Cahiers du GERAD (2009) G-2009-64] conjectured that the distance energy of a complete multipartite graph of order n with r ≥ 2 parts, each of size at least 2, is equal to 4(n − r). Stevanovic, Milosevic, Hic and Pokorny in [MATCH Commun. Math. Comput. Chem. 70 (2013), no. 1, 157-162.] proved the conjecture, and then Zhang in [Linear Algebra Appl. 450 (2014), 108-120.] gave another proof. We give a shorter proof of this conjecture using the interlacing inequalities...
A simple derivation of the eigenvalues of a tridiagonal matrix arising in biogeography
In investigating a certain optimization problem in biogeography, Simon [IEEE Trans. Evolutionary Comput. 12 (2008), 702-713] encountered a certain specially structured tridiagonal matrix and made a conjecture regarding its eigenvalues. A few years later, the validity of the conjecture was established by Igelnik and Simon [Appl. Math. Comput. 218 (2011), 195-201]. In this paper, we give another proof of this conjecture that is much shorter, almost computation-free, and does not resort to the eigenvectors...
A simple method for estimating the bounds of spectral radius of nonnegative irreducible matrices.
A sparsity result on nonnegative real matrices with given spectrum
Let σ=(λ1,...,λn) be the spectrum of a nonnegative real n × n matrix. It is shown that σ is the spectrum of a nonnegative real n × n matrix having at most nonzero entries.
A Spectral Theory for Tensors
In this paper we propose a general spectral theory for tensors. Our proposed factorization decomposes a tensor into a product of orthogonal and scaling tensors. At the same time, our factorization yields an expansion of a tensor as a summation of outer products of lower order tensors. Our proposed factorization shows the relationship between the eigen-objects and the generalised characteristic polynomials. Our framework is based on a consistent multilinear algebra which explains how to generalise...
A strategy for proving Riemann hypothesis.
A sufficient condition for Hurwitz stability of the convex combination of two matrices
A survey of some recent results on Clifford algebras in
We will study applications of numerical methods in Clifford algebras in , in particular in the skew field of quaternions, in the algebra of coquaternions and in the other nondivision algebras in . In order to gain insight into the multidimensional case, we first consider linear equations in quaternions and coquaternions. Then we will search for zeros of one-sided (simple) quaternion polynomials. Three different classes of zeros can be distinguished. In general, the quaternionic coefficients can...
A Trace Inequality of John von Neumann.
A Unified Extension of Some Results of Thompson, Marcus and Moyls.
A variant on the graph parameters of Colin de Verdière: implications to the minimum rank of graphs.
AB-Algorithm and Its Modifications for the Spectral Problems of Linear Pencils of Matrices.
Acyclic digraphs and eigenvalues of -matrices.
Algebraic conditions for -tough graphs
We give some algebraic conditions for -tough graphs in terms of the Laplacian eigenvalues and adjacency eigenvalues of graphs.
Algebraic Connections Between the Least Squares and Total Least Squares Problems.