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41.
AN ALGORITHM FOR JORDAN CANONICAL FORM OF A QUATERNION MATRIX 总被引:2,自引:0,他引:2
In this paper, we first introduce a concept of companion vector, and study the Jordan canonical forms of quaternion matrices by using the methods of complex rep resentation and companion vector, not only give out a practical algorithm for Jordan canonical form J of a quaternion matrix A, but also provide a practical algorithm for corresponding nonsingular matrix P with P-1AP = J. 相似文献
42.
体上右线性方程组的反问题 总被引:1,自引:0,他引:1
设F,K,Ω分别表示一个任意的体、一个具有对合反自同构的体和一个实四元数体,Fn表示F上的n维右向量空间.本文推广和改进了实线性方程组的反问题及一系列结果,解决了F上右线性方程组更具一般性的反问题(简称IPS):给定b∈Fs和αi∈Fn(i=1,…,m≤n)满足rank[α1,…,αm]=m,求所有的s×n矩阵A使Aαi=b(i=1,…,m).当s=n时 相似文献
43.
Stuart G. Hoggar 《Geometriae Dedicata》1998,69(3):287-289
An earlier computer calculation produced the vertices of a polytope in quaternionic 4-space, and determined their mutual angles all to be arccos (1/3). This note establishes a computer-independent verification. 相似文献
44.
An anti-torus is a subgroup 〈a,b 〉 in the fundamental group of a compact non-positively curved space X, acting in a specific way on the universal covering space X such that a and b do not have any commuting nontrivial powers. We construct and investigate anti-tori in a class of commutative transitive fundamental groups of finite square complexes, in particular for the groups Γp,l originally studied by Mozes [Israel J. Math. 90(1–3) (1995), 253–294]. It turns out that anti-tori in Γp,l directly correspond to non commuting pairs of Hamilton quaternions. Moreover, free anti-tori in Γp,l are related to free groups generated by two integer quaternions, and also to free subgroups of
. As an application, we prove that the multiplicative group generated by the two quaternions 1+2i and 1+4k is not free. 相似文献
45.
褚玉明 《数学物理学报(B辑英文版)》2005,25(3):492-504
The main aim of this paper is to discuss the following two problems:λm)∈Hm×m, find A ∈ BSH≥n×n such that AX= X∧, where BSH≥n×n denotes the set of all n × n quaternion matrices which are bi-self-conjugate and nonnegative definite.Problem Ⅱ:Given B ∈ Hn×m, find -B∈SE such that ||B- B||Q = minA∈sE ||B - A||Q,necessary and sufficient conditions for SE being nonempty are obtained. The general form of elements in SE and the expression of the unique solution B of problem Ⅱ are given. 相似文献
46.
《Mathematical Methods in the Applied Sciences》2018,41(12):4491-4505
A map is an involution (resp, anti‐involution) if it is a self‐inverse homomorphism (resp, antihomomorphism) of a field algebra. The main purpose of this paper is to show how split semi‐quaternions can be used to express half‐turn planar rotations in 3‐dimensional Euclidean space and how they can be used to express hyperbolic‐isoclinic rotations in 4‐dimensional semi‐Euclidean space . We present an involution and an anti‐involution map using split semi‐quaternions and give their geometric interpretations as half‐turn planar rotations in . Also, we give the geometric interpretation of nonpure unit split semi‐quaternions, which are in the form p = coshθ + sinhθ i + 0 j + 0 k = coshθ + sinhθ i , as hyperbolic‐isoclinic rotations in . 相似文献
47.
Gang Wang Zhenwei Guo Dong Zhang Tongsong Jiang 《Mathematical Methods in the Applied Sciences》2020,43(3):1124-1137
This paper aims to present, in a unified manner, algebraic techniques for least squares problem in quaternionic and split quaternionic mechanics. This paper, by means of a complex representation and a real representation of a generalized quaternion matrix, studies generalized quaternion least squares (GQLS) problem, and derives two algebraic methods for solving the GQLS problem. This paper gives not only algebraic techniques for least squares problem over generalized quaternion algebras, but also a unification of algebraic techniques for least squares problem in quaternionic and split quaternionic theory. 相似文献
48.
Emna Tefjeni 《Integral Transforms and Special Functions》2020,31(8):669-684
ABSTRACT In this paper, we present some new elements of harmonic analysis related to the right-sided multivariate continuous quaternion wavelet transform. The main objective of this article is to introduce the concept of the right-sided multivariate continuous quaternion wavelet transform and investigate its different properties using the machinery of multivariate quaternion Fourier transform. Last, we have proven a number of uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform. 相似文献
49.
This article is a continuation of the article [F. Zhang, Ger?gorin type theorems for quaternionic matrices, Linear Algebra Appl. 424 (2007), pp. 139–153] on the study of the eigenvalues of quaternion matrices. Profound differences in the eigenvalue problems for complex and quaternion matrices are discussed. We show that Brauer's theorem for the inclusion of the eigenvalues of complex matrices cannot be extended to the right eigenvalues of quaternion matrices. We also provide necessary and sufficient conditions for a complex square matrix to have infinitely many left eigenvalues, and analyse the roots of the characteristic polynomials for 2?×?2 matrices. We establish a characterisation for the set of left eigenvalues to intersect or be part of the boundary of the quaternion balls of Ger?gorin. 相似文献
50.