共查询到20条相似文献,搜索用时 31 毫秒
1.
Carlos Gamas 《Linear and Multilinear Algebra》2000,47(2):151-173
Let λ be an irreducible character of Sn corresponding to the partition (r,s) of n. Let A be a positive semidefinite Hermitian n × n matrix. Let dλ(A) and per(A) be the immanants corresponding to λ and to the trivial character of Sn, respectively. A proof of the inequality dλ(A)≤λ(id)per(A) is given. 相似文献
2.
Raphael Loewy 《Linear and Multilinear Algebra》1993,36(2):115-123
We prove the following result. Let F be an infinite field of characteristic other than two. Let k be a positive integer. Let Sn(F) denote the space of all n × n symmetric matrices with entries in F, and let T:Sn(F)→Sn(F) be a linear operator. Suppose that T is rank-k nonincreasing and its image contains a matrix with rank higher than K. Then, there exist λεF and PεFn,n such that T(A)=λPAPt for all AεSn(F). λ can be chosen to be 1 if F is algebraically closed and ±1 if F=R, the real field. 相似文献
3.
We give criterions for a flat portion to exist on the boundary of the numerical range of a matrix. A special type of Teoplitz matrices with flat portions on the boundary of its numerical range are constructed. We show that there exist 2 × 2 nilpotent matrices A1,A2, an n × n nilpotent Toeplitz matrix Nn, and an n × n cyclic permutation matrix Sn(s) such that the numbers of flat portions on the boundaries of W(A1⊕Nn) and W(A2⊕Sn(s)) are, respectively, 2(n - 2) and 2n. 相似文献
4.
We consider scalar-valued matrix functions for n×n matrices A=(aij) defined by Where G is a subgroup of Sn the group of permutations on n letters, and χ is a linear character of G. Two such functions are the permanent and the determinant. A function (1) is multiplicative on a semigroup S of n×n matrices if d(AB)=d(A)d(B) AB∈S.
With mild restrictions on the underlying scalar ring we show that every element of a semigroup containing the diagonal matrices on which (1) is multiplicative can have at most one nonzero diagonal(i.e., diagonal with all nonzero entries)and conversely, provided that χ is the principal character(χ≡1). 相似文献
With mild restrictions on the underlying scalar ring we show that every element of a semigroup containing the diagonal matrices on which (1) is multiplicative can have at most one nonzero diagonal(i.e., diagonal with all nonzero entries)and conversely, provided that χ is the principal character(χ≡1). 相似文献
5.
Raphael Loewy 《Linear and Multilinear Algebra》2001,48(4):355-382
Let k and n be positive integers such that k≤n. Let Sn(F) denote the space of all n×n symmetric matrices over the field F with char F≠2. A subspace L of Sn(F) is said to be a k-subspace if rank A≤k for every AεL.
Now suppose that k is even, and write k=2r. We say a k∥-subspace of Sn(F) is decomposable if there exists in Fn a subspace W of dimension n-r such that xtAx=0 for every xεWAεL.
We show here, under some mild assumptions on kn and F, that every k∥-subspace of Sn(F) of sufficiently large dimension must be decomposable. This is an analogue of a result obtained by Atkinson and Lloyd for corresponding subspaces of Fm,n. 相似文献
Now suppose that k is even, and write k=2r. We say a k∥-subspace of Sn(F) is decomposable if there exists in Fn a subspace W of dimension n-r such that xtAx=0 for every xεWAεL.
We show here, under some mild assumptions on kn and F, that every k∥-subspace of Sn(F) of sufficiently large dimension must be decomposable. This is an analogue of a result obtained by Atkinson and Lloyd for corresponding subspaces of Fm,n. 相似文献
6.
Inertially arbitrary patterns 总被引:11,自引:0,他引:11
An n×n sign pattern matrix A is an inertially arbitrary pattern (IAP) if each non-negative triple (rst) with r+s+t=n is the inertia of a matrix with sign pattern A. This paper considers the n×n(n≥2) skew-symmetric sign pattern Sn with each upper off-diagonal entry positive, the (1,1) entry negative, the (nn) entry positive, and every other diagonal entry zero. We prove that Sn is an IAP. 相似文献
7.
Xian Zhang 《Linear and Multilinear Algebra》2004,52(5):349-358
Suppose F is a field of characteristic not 2. Let MnF and SnF be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from SnF to SnF (respectively, MnF) preserving Moore-Penrose inverses of matrices are characterized. We first characterize all additive Moore-Penrose inverse preserving maps from SnF to MnF, and thereby, all additive Moore-Penrose inverse preserving maps from SnF to itself are characterized by restricting the range of these additive maps into the symmetric matrix space. 相似文献
8.
A polynomial in two variables is defined by Cn(x,t)=ΣπΠnx(Gπ,x)t|π|, where Πn is the lattice of partitions of the set {1, 2, …, n}, Gπ is a certain interval graph defined in terms of the partition gp, χ(Gπ, x) is the chromatic polynomial of Gπ and |π| is the number of blocks in π. It is shown that , where S(n, i) is the Stirling number of the second kind and (x)i = x(x − 1) ··· (x − i + 1). As a special case, Cn(−1, −t) = An(t), where An(t) is the nth Eulerian polynomial. Moreover, An(t)=ΣπΠnaπt|π| where aπ is the number of acyclic orientations of Gπ. 相似文献
9.
From GCH and Pm(κ)-hypermeasurable (1 <m<gw), we construct a model satisfying 2n = a(n) and 2ω = ω+m for a monotone a:ω→ω satisfying a(n)>n. 相似文献
10.
Chi-Kwong Li Ilya Spitkovsky Sudheer Shukla 《Linear algebra and its applications》1998,270(1-3):323-349
Let Mn be the algebra of all n × n complex matrices. For 1 k n, the kth numerical range of A Mn is defined by Wk(A) = (1/k)∑jk=1xj*Axj : x1, …, xk is an orthonormal set in n]. It is known that tr A/n = Wn(A) Wn−1(A) W1(A). We study the condition on A under which Wm(A) = Wk(A) for some given 1 m < k n. It turns out that this study is closely related to a conjecture of Kippenhahn on Hermitian pencils. A new class of counterexamples to the conjecture is constructed, based on the theory of the numerical range. 相似文献
11.
A holey Schröder design of type h1n1h2n2 … hknk (HSD(h1n1h2n2 … hknk)) is equivalent to a frame idempotent Schröder quasigroup (FISQ(h1n1h2n2 … hknk)) of order n with ni missing subquasigroups (holes) of order hi, (1 i k), which are disjoint and spanning, that is, Σ1 i k nihi = n. In this paper, it is shown that an HSD(hn) exists if and only if h2n(n − 1) 0 (mod 4) with expceptions (h, n) ε {{(1,5),(1,9),(2,4)}} and the possible exception of (h, n) = (6,4). 相似文献
12.
13.
This note proves a conjecture of Merris that the minimal value of entries of the doubly stochastic matrix of the degree antiregular graph En of order n ≥ 3 is equal to (l/2(n + l)). 相似文献
14.
Morris Newman 《Linear and Multilinear Algebra》1982,11(4):363-366
Let Rbe a principal ideal ringRn the ring of n× nmatrices over R, and dk(A) the kth determinantal divisor of Afor 1 ≤ k≤ n, where Ais any element of Rn, It is shown that if A,BεRn, det(A) det(B:) ≠ 0, then dk(AB) ≡ 0 mod dk(A) dk(B). If in addition (det(A), det(B)) = 1, then it is also shown that dk(AB) = dk(A) dk(B). This provides a new proof of the multiplicativity of the Smith normal form for matrices with relatively prime determinants. 相似文献
15.
Let (Sn) be the sequence given by the Jacobi-Gauss quadrature method when the integrand is an analytic function with a lopatilluric singularity or with a branch point on the real axis, and S its limi. We give an asymptotic representation of the errors S − Sn and of Sn+s − Sn, which leads to building other sequences which give a better approximation of the exact value of the integral than Sn. All the results are illustrated by numerical examples. 相似文献
16.
Let n = n1 + n2 + … + nj a partition Π of n. One will say that this partition represents the integer a if there exists a subsum nil + ni2 + … + nil equal to a. The set
(Π) is defined as the set of all integers a represented by Π. Let
be a subset of the set of positive integers. We denote by p(
,n) the number of partitions of n with parts in
, and by
((
,n) the number of distinct sets represented by these partitions. Various estimates for
(
,n) are given. Two cases are more specially studied, when
is the set {1, 2, 4, 8, 16, …} of powers of 2, and when
is the set of all positive integers. Two partitions of n are said to be equivalent if they represent the same integers. We give some estimations for the minimal number of parts of a partition equivalent to a given partition. 相似文献
17.
It is shown that the minimum value of the permanent on the n× ndoubly stochastic matrices which contain at least one zero entry is achieved at those matrices nearest to Jnin Euclidean norm, where Jnis the n× nmatrix each of whose entries is n-1. In case n ≠ 3 the minimum permanent is achieved only at those matrices nearest Jn; for n= 3 it is achieved at other matrices containing one or more zero entries as well. 相似文献
18.
Vincent P. Gallagher 《Linear and Multilinear Algebra》1979,7(2):167-174
Let F be a local field of characteristic ≠2 and K a Galois extension field of F of degree n. Then K can be viewed as a quadratic space over F under the bilinear form T(xy)=trK/Fxy for xyεK. The invariants of this form are given in the case when n is odd; when n is even and F is nondyadic; and when n is evesF dyadic, and K/F is unramifed. 相似文献
19.
A mapping ƒ : n=1∞In → I is called a bag mapping having the self-identity if for every (x1,…,xn) ε i=1∞In we have (1) ƒ(x1,…,xn) = ƒ(xi1,…,xin) for any arrangement (i1,…,in) of {1,…,n}; monotonic; (3) ƒ(x1,…,xn, ƒ(x1,…,xn)) = ƒ(x1,…,xn). Let {ωi,n : I = 1,…,n;n = 1,2,…} be a family of non-negative real numbers satisfying Σi=1nωi,n = 1 for every n. Then one calls the mapping ƒ : i=1∞In → I defined as follows an OWA bag mapping: for every (x1,…,xn) ε i=1∞In, ƒ(x1,…,xn) = Σi=1nωi,nyi, where yi is the it largest element in the set {x1,…,xn}. In this paper, we give a sufficient and necessary condition for an OWA bag mapping having the self-identity. 相似文献
20.
Let Fm × n be the set of all m × n matrices over the field F = C or R Denote by Un(F) the group of all n × n unitary or orthogonal matrices according as F = C or F-R. A norm N() on Fm ×n, is unitarily invariant if N(UAV) = N(A): for all A ∈ F m×n U ∈ Um(F). and V ∈ Un(F). We characterize those linear operators TFm × n → Fm × nwhich satisfy N (T(A)) = N(A)for all A ∈ Fm × n
for a given unitarily invariant norm N(). It is shown that the problem is equivalent to characterizing those operators which preserve certain subsets in Fm × n To develop the theory we prove some results concerning unitary operators on Fm × n which are of independent interest. 相似文献
for a given unitarily invariant norm N(). It is shown that the problem is equivalent to characterizing those operators which preserve certain subsets in Fm × n To develop the theory we prove some results concerning unitary operators on Fm × n which are of independent interest. 相似文献