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1.
具有奇异值分解性质的代数 总被引:4,自引:0,他引:4
设F为一个域,R为一个带有对合的F-代数,如果R上每一个矩阵都有奇异值分解(简称SVD),则称R为一个有SVD性质的F-代数.本文指出:R为一个有SVD性质的F-代数的充要条件是:R同构于R~+,或R~+上二次扩域,或R~+上四元数体((-1,-1)/R~+),其中R~+为R的对称元集合,并且R~+为一个Galois序闭域. 相似文献
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Jiang Tongsong Liu Yonghui Wei Musheng 《高校应用数学学报(英文版)》2006,21(1):113-118
This paper derives a theorem of generalized singular value decomposition of quaternion matrices (QGSVD),studies the solution of general quaternion matrix equation AXB -CYD= E,and obtains quaternionic Roth's theorem. This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation. 相似文献
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We show that the complex projection of a completely positive quaternionic map of quaternionic density matrices is a positive
map in the space of complex density matrices, and we briefly outline some of its properties. To illustrate this result, we
study the complex projection of a one-parameter quaternionic unitary dynamics of a spin-1/2 quantum system.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 360–370, June, 2007. 相似文献
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Robyn Pierce Kaye Stacey 《International Journal of Computers for Mathematical Learning》2004,9(1):59-93
This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
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Robust quantization watermarking with perceptual JND model has made a great success for image copyright protection. Generally, either restores each color channel separately or processes the vector representation from three color channels with the traditional monochromatic model. And it cannot make full use of the high correlation among RGB channels. In this paper, we proposed a robust quaternion JND Model for color image watermarking (QuatJND). In contrast to the existing perceptual JND models, the advantage of QuatJND is that it can integrate quaternion representation domain and colorfulness simultaneously, and QuatJND incorporates the pattern guided contrast masking effect in quaternion domain. On the other hand, in order to efficiently utilize the color information, we further develop a robust quantization watermarking framework using the color properties of the quaternion DCT coefficients in QuatJND. And the quantization steps of each quaternion DCT block in the scheme are optimal. Experimental results show that our method has a good performance in term of robustness with better visual quality. 相似文献
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浮心相当于浮体的支承点,其位置随物体的姿态而变化;物体稳定平衡时重心与浮心的距离达到极小。圆柱浮体有2~5个平衡位置,其中相间的1~2个稳定,其姿态与比重和长径比相关,在系统参数变化时可能突变。 相似文献
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