Several matrix Euclidean norm inequalities involving Kantorovich inequality.
Several results on chordal bipartite graphs
The question of generalizing results involving chordal graphs to similar concepts for chordal bipartite graphs is addressed. First, it is found that the removal of a bisimplicial edge from a chordal bipartite graph produces a chordal bipartite graph. As consequence, occurance of arithmetic zeros will not terminate perfect Gaussian elimination on sparse matrices having associated a chordal bipartite graph. Next, a property concerning minimal edge separators is presented. Finally, it is shown that,...
Sharp lower bounds for the dimension of linearizations of matrix polynomials.
Sharp Upper Bounds on the Signless Laplacian Spectral Radius of Strongly Connected Digraphs
Let G = (V (G),E(G)) be a simple strongly connected digraph and q(G) be the signless Laplacian spectral radius of G. For any vertex vi ∈ V (G), let d+i denote the outdegree of vi, m+i denote the average 2-outdegree of vi, and N+i denote the set of out-neighbors of vi. In this paper, we prove that: (1) (1) q(G) = d+1 +d+2 , (d+1 ≠ d+2) if and only if G is a star digraph [...] ,where d+1, d+2 are the maximum and the second maximum outdegree, respectively [...] is the digraph on n vertices obtained...
Shells of matrices in indefinite inner product spaces.
Short proofs of theorems of Mirsky and Horn on diagonals and eigenvalues of matrices.
Sign patterns that allow eventual positivity.
Sign patterns that require a positive or nonnegative left inverse.
Sign patterns that require eventual positivity or require eventual nonnegativity.
Sign patterns that require or allow power-positivity.
Signatura of magic and Latin integer squares: isentropic clans and indexing
The 2010 study of the Shannon entropy of order nine Sudoku and Latin square matrices by Newton and DeSalvo [Proc. Roy. Soc. A 2010] is extended to natural magic and Latin squares up to order nine. We demonstrate that decimal and integer measures of the Singular Value sets, here named SV clans, are a powerful way of comparing different integer squares. Several complete sets of magic and Latin squares are included, including the order eight Franklin subset which is of direct relevance...
Sign-consistency and solvability of constrained linear systems.
Similarities of discrete and continuous Sturm-Liouville problems.
Simple conditions for practical stability of positive fractional discrete-time linear systems
In the paper the problem of practical stability of linear positive discrete-time systems of fractional order is addressed. New simple necessary and sufficient conditions for practical stability and for practical stability independent of the length of practical implementation are established. It is shown that practical stability of the system is equivalent to asymptotic stability of the corresponding standard positive discrete-time systems of the same order. The discussion is illustrated with numerical...
Simple multilinear algebras and hermitian operators
The paper studies multilinear algebras, known as comtrans algebras, that are determined by so-called -Hermitian matrices over an arbitrary field. The main result of this paper shows that the comtrans algebra of -dimensional -Hermitian matrices furnishes a simple comtrans algebra.
Simultaneous complements in n-spaces - an elementary proof
Simultaneous Iteration for Computing Invariant Subspaces of Non-Hermitian Matrices.
Simultaneous solution of linear equations and inequalities in max-algebra
Let and for . Max-algebra is an analogue of linear algebra developed on the pair of operations extended to matrices and vectors. The system of equations and inequalities have each been studied in the literature. We consider a problem consisting of these two systems and present necessary and sufficient conditions for its solvability. We also develop a polynomial algorithm for solving max-linear program whose constraints are max-linear equations and inequalities.
Simultaneous solutions of operator Sylvester equations
We consider simultaneous solutions of operator Sylvester equations (1 ≤ i ≤ k), where and are commuting k-tuples of bounded linear operators on Banach spaces and ℱ, respectively, and is a (compatible) k-tuple of bounded linear operators from ℱ to , and prove that if the joint Taylor spectra of and do not intersect, then this system of Sylvester equations has a unique simultaneous solution.
Sincere posets of finite prinjective type with three maximal elements and their sincere prinjective representations
Assume that K is an arbitrary field. Let (I,⪯) be a poset of finite prinjective type and let KI be the incidence K-algebra of I. A classification of all sincere posets of finite prinjective type with three maximal elements is given in Theorem 2.1. A complete list of such posets consisting of 90 diagrams is presented in Tables 2.2. Moreover, given any sincere poset I of finite prinjective type with three maximal elements, a complete set of pairwise non-isomorphic sincere indecomposable prinjective...