共查询到20条相似文献,搜索用时 31 毫秒
1.
The paper contains some general theorems for Hadamard product of matrices which in particular include Fiedler's Theorem and a better bound for an inequality on product of eigenvalues of certain matrices due to Ando. Lieb's concavity Theorem has been proved using operator means. Some inequalities for unitarily invariant norms have also been proved. 相似文献
2.
Chris Fuller 《Journal of Pure and Applied Algebra》2011,215(5):1116-1126
The Cartan-Dieudonné-Scherk Theorem states that for fields of characteristic other than 2, every orthogonality can be written as the product of a certain minimal number of reflections across hyperplanes. The earliest proofs are not constructive, and constructive proofs either do not achieve minimal results or have been restricted to special cases. This paper presents a constructive proof in the real or complex field of the decomposition of a generalized orthogonal matrix into the product of the minimal number of generalized Householder matrices. 相似文献
3.
Summary This note is related to an earlier paper by Bhatia, Davis, and Kittaneh [4]. For matrices similar to Hermitian, we prove an
inequality complementary to the one proved in [4, Theorem 3]. We also disprove a conjecture made in [4] about the norm of
a commutator.
This work was done when the first author visited the SFB 343 at University of Bielefeld in May and June 1994. 相似文献
4.
We use the Hilbert?s Nullstellensatz (Hilbert?s Zero Point Theorem) to give a direct proof of the formula for the determinants of the products of tensors. By using this determinant formula and using tensor product to represent the transformations of the slices of tensors, we prove some basic properties of the determinants of tensors which are the generalizations of the corresponding properties of the determinants for matrices. We also study the determinants of tensors after two types of transposes. We use the permutational similarity of tensors to discuss the relation between weakly reducible tensors and the triangular block tensors, and give a canonical form of the weakly reducible tensors. 相似文献
5.
Tu Boxun 《数学年刊B辑(英文版)》1982,3(2):249-259
Let \Omega be a field, and let F denote the Frobenius matrix:
$[F = \left( {\begin{array}{*{20}{c}}
0&{ - {\alpha _n}}\{{E_{n - 1}}}&\alpha
\end{array}} \right)\]$
where \alpha is an n-1 dimentional vector over Q, and E_n- 1 is identity matrix over \Omega.
Theorem 1. There hold two elementary decompositions of Frobenius matrix:
(i) F=SJB,
where S, J are two symmetric matrices, and B is an involutory matrix;
(ii) F=CQD,
where O is an involutory matrix, Q is an orthogonal matrix over \Omega, and D is a
diagonal matrix.
We use the decomposition (i) to deduce the following two theorems:
Theorem 2. Every square matrix over \Omega is a product of twe symmetric matrices
and one involutory matrix.
Theorem 3. Every square matrix over \Omega is a product of not more than four
symmetric matrices.
By using the decomposition (ii), we easily verify the following
Theorem 4(Wonenburger-Djokovic') . The necessary and sufficient condition
that a square matrix A may be decomposed as a product of two involutory matrices is
that A is nonsingular and similar to its inverse A^-1 over Q (See [2, 3]).
We also use the decomosition (ii) to obtain
Theorem 5. Every unimodular matrix is similar to the matrix CQB, where
C, B are two involutory matrices, and Q is an orthogonal matrix over Q.
As a consequence of Theorem 5. we deduce immediately the following
Theorem 6 (Gustafson-Halmos-Radjavi). Every unimodular matrix may be
decomposed as a product of not more than four involutory matrices (See [1] ).
Finally, we use the decomposition (ii) to derive the following
Thoerem 7. If the unimodular matrix A possesses one invariant factor which
is not constant polynomial, or the determinant of the unimodular matrix A is I and
A possesses two invariant factors with the same degree (>0), then A may be
decomposed as a product of three involutory matrices.
All of the proofs of the above theorems are constructive. 相似文献
6.
The authors obtain new characterizations of unconditional Cauchy series in termsof separation properties of subfamilies of P(N), and a generalization of the Orlicz-PettisTheorem is also obtained. New results on the uniform convergence on matrices anda new version of the Hahn-Schur summation theorem are proved. For matrices whoserows define unconditional Cauchy series, a better sufficient condition for the basicMatrix Theorem of Antosik and Swartz, new necessary conditions and a new proof ofthat theorem are given. 相似文献
7.
Leiba Rodman 《Linear algebra and its applications》2011,434(6):1513-1524
It is proved that a large class of matrix group actions, including joint similarity and congruence-like actions, as well as actions of the type of matrix equivalence, have local Lipschitz property. Under additional hypotheses, global Lipschitz property is proved. These results are specialized and applied to obtain local Lipschitz property of canonical bases of matrices that are selfadjoint in an indefinite inner product. Real, complex, and quaternionic matrices are considered. 相似文献
8.
The Flanders Theorem relates the matrices AB and BA and provides a necessary and sufficient condition for the consistency of the matrix system P = ABQ = BA In this paper, we generalize the Flanders condition for several matrices. 相似文献
9.
Riesz points of upper triangular operator matrices 总被引:1,自引:0,他引:1
Bruce A. Barnes 《Proceedings of the American Mathematical Society》2005,133(5):1343-1347
Two results are proved which concern Riesz points of upper triangular operator matrices. Applications are made to questions involving when Weyl's Theorem holds for an upper triangular operator matrix.
10.
11.
The Flanders Theorem relates the matrices AB and BA and provides a necessary and sufficient condition for the consistency of the matrix system P = AB Q = BA In this paper, we generalize the Flanders condition for several matrices. 相似文献
12.
指出了[1]的定理2中的一个错误,推广了[1]中定理1给出的华罗庚-王中烈型不等式,避开控制不等式与动态规划模型等专门工具,改用较为初等的平均值不等式证明之,使改正后的[1]中的定理2成其推论 相似文献
13.
The classical Brauer-Ostrowski Theorem gives a localization of the spectrum of a matrix by a union of Cassini ovals. In this
paper we prove a corresponding result for operator matrices. 相似文献
14.
Technical Note Discontinuous Implicit Quasivariational Inequalities in Normed Spaces 总被引:1,自引:0,他引:1
In this paper, we consider an implicit quasivariational inequality without continuity assumptions in normed spaces. The main
result (Theorem 2.1) provides an infinite-dimensional version of Theorem 3.2 in Ref. 1. To achieve such a goal, we employ
Theorem 3.2 in Ref. 1 and the technique of Cubiotti in Ref. 2. In particular, Theorem 3.1 covers a recent result of Cubiotti
(Theorem 3.1 of Ref. 2) as a special case.
Communicated by F. Giannessi
This research was partially supported by the National Science Council of Taiwan, ROC. 相似文献
15.
Intrinsic products and factorizations of matrices 总被引:1,自引:0,他引:1
Miroslav Fiedler 《Linear algebra and its applications》2008,428(1):5-13
We say that the product of a row vector and a column vector is intrinsic if there is at most one nonzero product of corresponding coordinates. Analogously we speak about intrinsic product of two or more matrices, as well as about intrinsic factorizations of matrices. Since all entries of the intrinsic product are products of entries of the multiplied matrices, there is no addition. We present several examples, together with important applications. These applications include companion matrices and sign-nonsingular matrices. 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.
《Discrete Mathematics》2022,345(6):112822
We consider a generalization of the Brauer-Wielandt-Harada Theorem to group-like regular association schemes. As an application, we give a necessary condition for commutative association schemes to be regular. Moreover, we derive the number of irreducible characters of multiplicity 1 from the product of all adjacency matrices and all valencies for a commutative regular association scheme. 相似文献
18.
Eung Chun Cho 《Applied Mathematics Letters》1991,4(6):51-53
Generalized forms of the Pythagorean Theorem for n-simplex are proved using the generalized cross product in Rn. 相似文献
19.