A remark on spaces over a special local ring
This paper deals with A-spaces in the sense of McDonald over linear algebras A of a certain type. Necessary and sufficient conditions for a submodule to be an A-space are derived.
A remark on the canonical form for a pair of orthoprojectors.
A remark on the Čebyšev property
A remark on the eigenvalues of generalized circulants
A remark on the quadratic analogue of the Quillen-Suslin theorem.
A representation of the minimal -norm solution.
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 resultant approach to computing vector characteristics of multiparameter polynomial matrices.
A review of Costas arrays.
A review of selected topics in majorization theory
In this expository paper, some recent developments in majorization theory are reviewed. Selected topics on group majorizations, group-induced cone orderings, Eaton triples, normal decomposition systems and similarly separable vectors are discussed. Special attention is devoted to majorization inequalities. A unified approach is presented for proving majorization relations for eigenvalues and singular values of matrices. Some methods based on the Chebyshev functional and similarly separable vectors...
A review of the matrix Riccati equation
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 cocyclic Jacket matrices.
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 simple proof of polar decomposition in pseudo-Euclidean geometry
We give a simple direct proof of the polar decomposition for separated linear maps in pseudo-Euclidean geometry.
A simple proof of the classification of normal Toeplitz matrices.
A Simple Proof of the Convexity of the Field of Values Defined by Two Hermitian Forms.