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861.
862.
863.
Let Tn (F) be the algebra of all n×n upper triangular matrices over an arbitrary field F. We first characterize those rank-one nonincreasing mappings ψ: Tn (F)→Tm (F)n?m such that ψ(In ) is of rank n. We next deduce from this result certain types of singular rank-one r-potent preservers and nonzero r-potent preservers on Tn (F). Characterizations of certain classes of homomorphisms and semi-homomorphisms on Tn (F) are also given. 相似文献
864.
865.
Helena ?migoc 《Linear and Multilinear Algebra》2013,61(2):85-96
This article presents a technique for combining two matrices, an n?×?n matrix M and an m?×?m matrix B, with known spectra to create an (n?+?m???p)?×?(n?+?m???p) matrix N whose spectrum consists of the spectrum of the matrix M and m???p eigenvalues of the matrix B. Conditions are given when the matrix N obtained in this construction is nonnegative. Finally, these observations are used to obtain several results on how to construct a realizable list of n?+?1 complex numbers (λ1,λ2,λ3,σ) from a given realizable list of n complex numbers (c 1,c 2,σ), where c 1 is the Perron eigenvalue, c 2 is a real number and σ is a list of n???2 complex numbers. 相似文献
866.
867.
Jacob Engwerda 《Linear and Multilinear Algebra》2013,61(6):689-700
In this note we consider the question under which conditions all entries of the matrix I???(I?+?X)?1 are nonnegative in case matrix X is a real positive definite matrix. Sufficient conditions are presented as well as some necessary conditions. One sufficient condition is that matrix X ?1 is an inverse M-matrix. A class of matrices for which the inequality holds is presented. 相似文献
868.
In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k?×?k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing. 相似文献
869.
Some well-known characterizations of nonnegative k-potent matrices have been obtained by Flor [P. Flor, On groups of nonnegative matrices, Compositio Math. 21 (1969), pp. 376–382.] and Jeter and Pye [M. Jeter and W. Pye, Nonnegative (s,?t)-potent matrices, Linear Algebra Appl. 45 (1982), pp. 109–121.]. In this article, we obtain a structural characterization of a real k-potent matrix A, provided that (sgn(A)) k+1 is unambiguously defined, regardless of whether A is nonnegative or not. 相似文献
870.
Zoran Z. Petrović 《Linear and Multilinear Algebra》2013,61(6):625-631
Motivated by the problem concerning the existence of non-singular bilinear maps, vector spaces of matrices consisting of matrices with rank bounded below are investigated. It is shown that bases for such spaces of maximum dimension can be chosen in such a way to consist of matrices of the minimal rank. An estimate of the ranks of matrices in particular types of bases for maximal such spaces is also given. This extends previously known results which were valid only in the case of spaces consisting of matrices of rank not equal to one. 相似文献