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Nonsingularity and P -matrices.

Jiří Rohn (1990)

Aplikace matematiky

New proofs of two previously published theorems relating nonsingularity of interval matrices to P -matrices are given.

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

Jiří Rohn (2007)

Applications of Mathematics

For a real square matrix A and an integer d ≥ 0 , let A ( d ) denote the matrix formed from A by rounding off all its coefficients to d decimal places. The main problem handled in this paper is the following: assuming that A ( d ) has some property, under what additional condition(s) can we be sure that the original matrix A possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists a real number...

Norm attaining bilinear forms on C*-algebras

J. Alaminos, R. Payá, A. R. Villena (2003)

Studia Mathematica

We give a sufficient condition on a C*-algebra to ensure that every weakly compact operator into an arbitrary Banach space can be approximated by norm attaining operators and that every continuous bilinear form can be approximated by norm attaining bilinear forms. Moreover we prove that the class of C*-algebras satisfying this condition includes the group C*-algebras of compact groups.

Norm estimates for solutions of matrix equations AX-XB=C and X-AXB=C

Michael I. Gil' (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Let A, B and C be matrices. We consider the matrix equations Y-AYB=C and AX-XB=C. Sharp norm estimates for solutions of these equations are derived. By these estimates a bound for the distance between invariant subspaces of matrices is obtained.

Note on a conjecture for the sum of signless Laplacian eigenvalues

Xiaodan Chen, Guoliang Hao, Dequan Jin, Jingjian Li (2018)

Czechoslovak Mathematical Journal

For a simple graph G on n vertices and an integer k with 1 ≤ k ≤ n , denote by 𝒮 k + ( G ) the sum of k largest signless Laplacian eigenvalues of G . It was conjectured that 𝒮 k + ( G ) ≤ e ( G ) + k + 1 2 , where e ( G ) is the number of edges of G . This conjecture has been proved to be true for all graphs when k ∈ { 1 , 2 , n - 1 , n } , and for trees, unicyclic graphs, bicyclic graphs and regular graphs (for all k ). In this note, this conjecture is proved to be true for all graphs when k = n - 2 , and for some new classes of graphs.

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