共查询到20条相似文献,搜索用时 0 毫秒
1.
In a recent paper, Neumann and Sze considered for an n × n nonnegative matrix A, the minimization and maximization of ρ(A + S), the spectral radius of (A + S), as S ranges over all the doubly stochastic matrices. They showed that both extremal values are always attained at an n × n permutation matrix. As a permutation matrix is a particular case of a normal matrix whose spectral radius is 1, we consider here, for positive matrices A such that (A + N) is a nonnegative matrix, for all normal matrices N whose spectral radius is 1, the minimization and maximization problems of ρ(A + N) as N ranges over all such matrices. We show that the extremal values always occur at an n × n real unitary matrix. We compare our results with a less recent work of Han, Neumann, and Tastsomeros in which the maximum value of ρ(A + X) over all n × n real matrices X of Frobenius norm was sought. 相似文献
2.
We provide a method for factoring all bounded ratios of the form
3.
C. Costara 《Linear algebra and its applications》2011,435(11):2674-2680
Let T be a continuous map of the space of complex n×n matrices into itself satisfying T(0)=0 such that the spectrum of T(x)-T(y) is always a subset of the spectrum of x-y. There exists then an invertible n×n matrix u such that either T(a)=uau-1 for all a or T(a)=uatu-1 for all a. We arrive at the same conclusion by supposing that the spectrum of x-y is always a subset of the spectrum of T(x)-Tt(y), without the continuity assumption on T. 相似文献
4.
We shall discuss geometric properties of a quadrangle with parallelogramic properties in a convex cone of positive definite matrices with respect to Thompson metric. 相似文献
5.
Henryk Minc 《Linear and Multilinear Algebra》1975,3(1):91-94
It is shown that if all subpermaneats of order k of an n × n doubly stochastic matrix are equal for some k ≤ n - 2, then all the entries of the matrix must be equal to 1/n. 相似文献
6.
Ádám Besenyei 《Linear algebra and its applications》2011,435(5):984-997
Some functions f:R+→R+ induce mean of positive numbers and the matrix monotonicity gives a possibility for means of positive definite matrices. Moreover, such a function f can define a linear mapping on matrices (which is basic in the constructions of monotone metrics). The present subject is to check the complete positivity of in the case of a few concrete functions f. This problem has been motivated by applications in quantum information. 相似文献
7.
Totally nonnegative matrices, i.e., matrices having all their minors nonnegative, and matrix intervals with respect to the checkerboard ordering are considered. It is proven that if the two bound matrices of such a matrix interval are nonsingular and totally nonnegative (and in addition all their zero minors are identical) then all matrices from this interval are also nonsingular and totally nonnegative (with identical zero minors). 相似文献
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A determinantal identity, frequently used in the study of totally positive matrices, is extended, and then used to re-prove the well-known univariate knot insertion formula for B-splines. Also we introduce a class of matrices, intermediate between totally positive and strictly totally positive matrices. The determinantal identity is used to show any minor of such matrices is positive if and only if its diagonal entries are positive. Among others, this class of matrices includes B-splines collocation matrices and Hurwitz matrices.This author acknowledges a sabbatical stay at IBM T.J. Watson Research Center in 1990, which was supported by a DGICYT grant from Spain. 相似文献
10.
Henryk Minc 《Linear and Multilinear Algebra》2013,61(1-2):91-94
It is shown that if all subpermaneats of order k of an n × n doubly stochastic matrix are equal for some k ≤ n ? 2, then all the entries of the matrix must be equal to 1/n. 相似文献
11.
Sergei? Sergeev 《Linear algebra and its applications》2009,431(8):1325-1757
In max algebra it is well known that the sequence of max algebraic powers Ak, with A an irreducible square matrix, becomes periodic after a finite transient time T(A), and the ultimate period γ is equal to the cyclicity of the critical graph of A.In this connection, we study computational complexity of the following problems: (1) for a given k, compute a periodic power Ar with and r?T(A), (2) for a given x, find the ultimate period of {Al⊗x}. We show that both problems can be solved by matrix squaring in O(n3logn) operations. The main idea is to apply an appropriate diagonal similarity scaling A?X-1AX, called visualization scaling, and to study the role of cyclic classes of the critical graph. 相似文献
12.
An n×m real matrix A is said to be totally positive (strictly totally positive) if every minor is nonnegative (positive). In this paper, we study characterizations of these classes of matrices by minors, by their full rank factorization and by their thin QR factorization. 相似文献
13.
Miroslav Fiedler 《Linear algebra and its applications》2006,413(1):177-188
A real matrix is called k-subtotally positive if the determinants of all its submatrices of order at most k are positive. We show that for an m × n matrix, only mn inequalities determine such class for every k, 1 ? k ? min(m,n). Spectral properties of square k-subtotally positive matrices are studied. Finally, completion problems for 2-subtotally positive matrices and their additive counterpart, the anti-Monge matrices, are investigated. Since totally positive matrices are 2-subtotally positive as well, the presented necessary conditions for this completion problem are also necessary conditions for totally positive matrices. 相似文献
14.
Glenn Merlet 《Linear algebra and its applications》2010,432(8):1923-1757
We investigate the action of semigroups of d×d matrices with entries in the max-plus semifield on the max-plus projective space. Recall that semigroups generated by one element with projectively bounded image are projectively finite and thus contain idempotent elements.In terms of orbits, our main result states that the image of a minimal orbit by an idempotent element of the semigroup with minimal rank has at most d! elements. Moreover, each idempotent element with minimal rank maps at least one orbit onto a singleton.This allows us to deduce the central limit theorem for stochastic recurrent sequences driven by independent random matrices that take countably many values, as soon as the semigroup generated by the values contains an element with projectively bounded image. 相似文献
15.
We define a new average - termed the resolvent average - for positive semidefinite matrices. For positive definite matrices, the resolvent average enjoys self-duality and it interpolates between the harmonic and the arithmetic averages, which it approaches when taking appropriate limits. We compare the resolvent average to the geometric mean. Some applications to matrix functions are also given. 相似文献
16.
Mark-Alexander Henn 《Linear algebra and its applications》2010,433(6):1055-1059
Complex matrices that are structured with respect to a possibly degenerate indefinite inner product are studied. Based on earlier works on normal matrices, the notions of hyponormal and strongly hyponormal matrices are introduced. A full characterization of such matrices is given and it is shown how those matrices are related to different concepts of normal matrices in degenerate inner product spaces. Finally, the existence of invariant semidefinite subspaces for strongly hyponormal matrices is discussed. 相似文献
17.
Roy Mathias 《Numerische Mathematik》1996,74(1):85-103
Summary. Let where is a positive definite matrix and is diagonal and nonsingular. We show that if the condition number of is much less than that of then we can use algorithms based on the Cholesky factorization of to compute the eigenvalues of to high relative accuracy more efficiently than by Jacobi's method. The new methods are generally slower than tridiagonalization
methods (which do not deliver the eigenvalues to maximal relative accuracy) but can be up to 4 times faster when the condition
number of is very large.
Received April 13, 1995 相似文献
18.
Siwen Guo 《Linear algebra and its applications》2007,426(1):199-203
Let σ=(ρ,b+ic,b-ic,λ4,…,λn) be the spectrum of an entry non-negative matrix and t?0. Laffey [T. J. Laffey, Perturbing non-real eigenvalues of nonnegative real matrices, Electron. J. Linear Algebra 12 (2005) 73-76] has shown that σ=(ρ+2t,b-t+ic,b-t-ic,λ4,…,λn) is also the spectrum of some nonnegative matrix. Laffey (2005) has used a rank one perturbation for small t and then used a compactness argument to extend the result to all nonnegative t. In this paper, a rank two perturbation is used to deduce an explicit and constructive proof for all t?0. 相似文献
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We consider an infinite lower triangular matrix L=[?n,k]n,k∈N0 and a sequence Ω=(ωn)n∈N0 called the (a,b)-sequence such that every element ?n+1,k+1 except lying in column 0 can be expressed as