共查询到20条相似文献,搜索用时 31 毫秒
1.
Marc Ensenbach 《Linear algebra and its applications》2010,432(11):2739-2744
Given three lists of ideals of a Dedekind domain, the question is raised whether there exist two matrices A and B with entries in the given Dedekind domain, such that the given lists of ideals are the determinantal divisors of A, B, and AB, respectively. To answer this question, necessary and sufficient conditions are developed in this article. 相似文献
2.
S.W. Drury 《Linear algebra and its applications》2007,422(1):318-325
We establish the following case of the Determinantal Conjecture of Marcus [M. Marcus, Derivations, Plücker relations and the numerical range, Indiana Univ. Math. J. 22 (1973) 1137-1149] and de Oliveira [G.N. de Oliveira, Research problem: Normal matrices, Linear and Multilinear Algebra 12 (1982) 153-154]. Let A and B be unitary n × n matrices with prescribed eigenvalues a1, … , an and b1, … , bn, respectively. Then for any scalars t and s
3.
Twisted inner products and contraction inequalities on spaces of contravariant and covariant tensors
Thomas H. Pate 《Linear algebra and its applications》2008,429(7):1489-1503
Given positive integers n and p, and a complex finite dimensional vector space V, we let Sn,p(V) denote the set of all functions from V×V×?×V-(n+p copies) to C that are linear and symmetric in the first n positions, and conjugate linear symmetric in the last p positions. Letting κ=min{n,p} we introduce twisted inner products, [·,·]s,t,1?s,t?κ, on Sn,p(V), and prove the monotonicity condition [F,F]s,t?[F,F]u,v is satisfied when s?u?κ,t?v?κ, and F∈Sn,p(V). Using the monotonicity condition, and the Cauchy-Schwartz inequality, we obtain as corollaries many known inequalities involving norms of symmetric multilinear functions, which in turn imply known inequalities involving permanents of positive semidefinite Hermitian matrices. New tensor and permanental inequalities are also presented. Applications to partial differential equations are indicated. 相似文献
4.
An n-by-n real matrix A enjoys the “leading implies all” (LIA) property, if, whenever D is a diagonal matrix such that A+D has positive leading principal minors (PMs), all PMs of A are positive. Symmetric and Z-matrices are known to have this property. We give a new class of matrices (“mixed matrices”) that both unifies and generalizes these two classes and their special diagonal equivalences by also having the LIA property. “Nested implies all” (NIA) is also enjoyed by this new class. 相似文献
5.
Some new lower bounds for the minimum eigenvalue of the Hadamard product of an M-matrix and its inverse are given. These bounds improve the results of [H.B. Li, T.Z. Huang, S.Q. Shen, H. Li, Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse, Linear Algebra Appl. 420 (2007) 235-247]. 相似文献
6.
Tanvi Jain 《Linear algebra and its applications》2011,435(5):1111-1121
In an earlier paper (R. Bhatia, T. Jain, Higher order derivatives and perturbation bounds for determinants, Linear Algebra Appl. 431 (2009) 2102-2108) we gave formulas for derivatives of all orders for the map that takes a matrix to its determinant. In this paper we continue that work, and find expressions for the derivatives of all orders for the antisymmetric tensor powers and for the coefficients of the characteristic polynomial. We then evaluate norms of these derivatives, and use them to obtain perturbation bounds. 相似文献
7.
Lower bounds for the minimum eigenvalue of Hadamard product of an M-matrix and its inverse 总被引:2,自引:0,他引:2
For the Hadamard product A ° A−1 of an M-matrix A and its inverse A−1, we give new lower bounds for the minimum eigenvalue of A ° A−1. These bounds are strong enough to prove the conjecture of Fiedler and Markham [An inequality for the Hadamard product of an M-matrix and inverse M-matrix, Linear Algebra Appl. 101 (1988) 1-8]. 相似文献
8.
Given a Jordan matrix J, we obtain an explicit formula for the determinant of any matrix T that commutes with it. 相似文献
9.
R.B. Bapat Sivaramakrishnan Sivasubramanian 《Linear algebra and its applications》2011,435(6):1479-1489
It is shown that if L and D are the Laplacian and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors of the complementary submatrix of D, up to sign and a power of 2. An analogous, more general result is proved for the Laplacian and the resistance matrix of any graph. A similar identity is proved for graphs in which each block is a complete graph on r vertices, and for q-analogues of such matrices of a tree. Our main tool is an identity for the minors of a matrix and its inverse. 相似文献
10.
Mikyoung Lim 《Journal of Differential Equations》2011,250(5):2402-2439
In stiff fiber-reinforced composites, it has been known that the shear stress increases at the rate of as the distance ? between adjacent fibers approaches 0. This paper reveals a strong influence of a combination of a triple fiber, as well as the distance between a pair of fibers, on the blow-up so that the stress concentration can be significantly accelerated by adding a small fiber in-between fibers. Specifically, if a fiber F2 with a small diameter δ is located in-between fibers F1 and F3, ?1=dist(F1,F2) and ?2=dist(F2,F3), then the stress blows up at the exact rates of and between F1 and F2 and between F2 and F3, respectively. This estimate still holds even when a part of F2 overlaps with F3. The magnification factor yields the enormous increase in the stress that greatly surpasses the expectancy by previous methods. 相似文献
11.
Miroslav Fiedler 《Linear algebra and its applications》2011,434(4):1189-1194
We study the class of so-called totally dominant matrices in the usual algebra and in the max algebra in which the sum is the maximum and the multiplication is usual. It turns out that this class coincides with the well known class of positive matrices having positive the determinants of all 2×2 submatrices. The closure of this class is closed not only with respect to the usual but also with respect to the max multiplication. Further properties analogous to those of totally positive matrices are proved and some connections to Monge matrices are mentioned. 相似文献
12.
Magdalena Wanat 《Linear algebra and its applications》2006,414(1):304-309
We generalize two results: Kraaijevanger’s 1991 characterization of diagonal stability via Hadamard products and the block matrix version of the closure of the positive definite matrices under Hadamard multiplication. We restate our generalizations in terms of Pα-matrices and α-scalar diagonally stable matrices. 相似文献
13.
Luis Verde-Star 《Linear algebra and its applications》2011,434(1):307-318
We use basic properties of infinite lower triangular matrices and the connections of Toeplitz matrices with generating-functions to obtain inversion formulas for several types of q-Pascal matrices, determinantal representations for polynomial sequences, and identities involving the q-Gaussian coefficients. We also obtain a fast inversion algorithm for general infinite lower triangular matrices. 相似文献
14.
Yongzhi Yang 《Linear algebra and its applications》2009,430(1):511-630
In this paper, we introduce the generalized Leibniz functional matrices and study some algebraic properties of such matrices. To demonstrate applications of these properties, we derive several novel factorization forms of some well-known matrices, such as the complete symmetric polynomial matrix and the elementary symmetric polynomial matrix. In addition, by applying factorizations of the generalized Leibniz functional matrices, we redevelop the known results of factorizations of Stirling matrices of the first and second kind and the generalized Pascal matrix. 相似文献
15.
Moshe Schwartz 《Linear algebra and its applications》2009,430(4):1364-1374
We present a new efficient method for computing the permanent and Hafnian of certain banded Toeplitz matrices. The method covers non-trivial cases for which previous known methods do not apply. The main idea is to use the elements of the first row and column, which determine the entire Toeplitz matrix, to construct a digraph in which certain paths correspond to permutations that the permanent and Hafnian count. Since counting paths can be done efficiently, the permanent and Hafnian for those matrices is easily obtainable. 相似文献
16.
V. Cortes 《Linear algebra and its applications》2010,432(8):1990-1994
An n×n real matrix is called sign regular if, for each k(1?k?n), all its minors of order k have the same nonstrict sign. The zero entries which can appear in a nonsingular sign regular matrix depend on its signature because the signature can imply that certain entries are necessarily nonzero. The patterns for the required nonzero entries of nonsingular sign regular matrices are analyzed. 相似文献
17.
Using the arithmetic-geometric mean inequality, we give bounds for k-subpermanents of nonnegative n×n matrices F. In the case k=n, we exhibit an n2-set S whose arithmetic and geometric means constitute upper and lower bounds for per(F)/n!. We offer sharpened versions of these bounds when F has zero-valued entries. 相似文献
18.
19.
Some new bounds on the spectral radius of matrices 总被引:2,自引:0,他引:2
A new lower bound on the smallest eigenvalue τ(AB) for the Fan product of two nonsingular M-matrices A and B is given. Meanwhile, we also obtain a new upper bound on the spectral radius ρ(A°B) for nonnegative matrices A and B. These bounds improve some results of Huang (2008) [R. Huang, Some inequalities for the Hadamard product and the Fan product of matrices, Linear Algebra Appl. 428 (2008) 1551-1559]. 相似文献
20.
Maozhong Fang 《Linear algebra and its applications》2007,425(1):7-15
We prove an upper bound for the spectral radius of the Hadamard product of nonnegative matrices and a lower bound for the minimum eigenvalue of the Fan product of M-matrices. These improve two existing results. 相似文献