On the period and base of a sign pattern matrix
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In this paper, the authors characterize irreducible powerful sign pattern matrices and investigate the period and base of such matrices, and give some significant classes of powerful patterns.About:
This article is published in Linear Algebra and its Applications.The article was published on 1994-11-15 and is currently open access. It has received 54 citations till now. The article focuses on the topics: Sign (mathematics) & Matrix (mathematics).read more
Citations
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A Mathematical Bibliography of Signed and Gain Graphs and Allied Areas
TL;DR: This is a bibliography of signed graphs and related mathematics, where work on weighted graphs are regarded as outside the scope of the bibliography — except (to some extent) when the author calls the weights "signs".
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Bounds on the bases of irreducible generalized sign pattern matrices
TL;DR: Li et al. as mentioned in this paper studied the bases for non-powerful irreducible sign pattern matrices and generalized sign patterns and obtained sharp upper bounds, together with a complete characterization of the equality cases, of the bases of such matrices.
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Potentially nilpotent sign pattern matrices
TL;DR: In this article, the sign patterns that allow nilpotence of index 2 are investigated and for orders up to three, potentially nilpotent tree sign patterns are also explored, and a number of qualitative necessary or sufficient conditions are established.
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Irreducible sign k-potent sign pattern matrices
TL;DR: In this paper, the structure of sign k-potent matrices was characterized for the reducible case, and necessary conditions were provided for each off-diagonal block of the Frobenius normal form of a reducible sign k -potent matrix.
References
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Book
Matrix Analysis
Roger A. Horn,Charles R. Johnson +1 more
TL;DR: In this article, the authors present results of both classic and recent matrix analyses using canonical forms as a unifying theme, and demonstrate their importance in a variety of applications, such as linear algebra and matrix theory.
Book
Combinatorial Matrix Theory
Richard A. Brualdi,H. J. Ryser +1 more
TL;DR: In this paper, the existence theorems for combinatorially constrained matrices are given for instance matrices, digraphs, bigraphs and Latin squares, as well as some special graphs.
Journal ArticleDOI
Sign patterns that require real, nonreal or pure imaginary eigenvalues
TL;DR: In this paper, the authors characterize the n-by-n sign pattern matrices that require all real, all nonreal, and all pure imaginary eigenvalues to have a positive real eigenvalue.
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Some outstanding problems in the theory of matrices
TL;DR: An informal personal survey of some major outstanding questions in matrix theory is given in this paper, which are grouped into several categories and illustrate the faci that modern work in matrix analysis relies predominantly on neither linear nor algebraic techniques.