JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (12): 81-86.doi: 10.6040/j.issn.1671-9352.0.2014.159

Previous Articles     Next Articles

Generalized singular value decompositions with respect to Semi-definite inner product

ZHENG Chan, LI Han-yu   

  1. College of Mathematics and Statistics, Chongqing University, Chongqing 401331, China
  • Received:2014-04-14 Revised:2014-11-07 Online:2014-12-20 Published:2014-12-20

PDF (PC)

704

Abstract: The generalized inverses of matrices were used to study the weighted singular value decomposition with one of the weight matrices being positive semi-definite and the other being positive definite. Some conditions for the existence of the generalized singular value decompositions with respect to a semi-definite inner product were also presented.

Key words: semi-definite, weighted, singular value decomposition, semi-definite inner product, generalized inverse of matrix

CLC Number: 

  • O151
[1] HASSI S. A singular value decomposition of matrices in a space with an indefinite scalar product[M]. Suomalainen Tiedeakatemia, 1990.
[2] ARIAS M L,COACH G, GONZALEZ M C. Partial isometrics in semi-Hilbertian spaces[J]. Linear Algebra and its Applications, 2008, 428(7):1460-1475.
[3] 孙继广.矩阵扰动分析[M].北京:科学出版社,2001:2-43. SUN Jiguang. Matrix perturbation analysis[M]. Beijing: Science Press, 2001:2-43.
[4] VAN LOAN C F. Generalizing the singular value decomposition[J]. SIAM Journal on Numerical Analysis, 1976, 13(1):76-83.
[5] STEWART G W. On the early history of the singular value decomposition[J]. SIAM Review, 1993, 35(4):551-566.
[6] ONN R, STEINHARDT A O, BOJANCZYK A W. The hyperbolic singular value decomposition and applications[J]. IEEE Transactions on Signal Processing, 1991, 39(7):1575-1588.
[7] ŠEGO V. Two-sided hyperbolic singular value decomposition[D]. Zagreb:University of Zagreb, 2009.
[8] 史存琴.广义双曲奇异值分解及在广义逆和不定最小二乘问题中的应用[D].甘肃:兰州大学,2011. SHI Cunqin. Generalized hyperbolic singular decompositions and applications in generalized inverse and indefinite least squares problems[D].Gansu: Lanzhou University, 2011.
[9] 孙文瑜.一般二次规划的广义逆解[J]. 高等学校计算数学学报, 1991,1(11):94-98. SUN Wenyu. Generalized inverses solution for general quadratic programming [J].Numerical Mathematics A Journal of Chinese Universities, 1991, 1(11):94-98.
[1] TAO Shuang-ping, GAO Rong. Estimates of multilinear fractional integrals and maximal operators on weighted Morrey spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 30-37.
[2] DENG Yi-hua. Estimates for the Hessian of f-harmonic functions and their applications to splitting theorem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 83-86.
[3] JIANG Long, CHEN Min. Jensens inequality, moment inequality and law of large numbers for weighted g-expectation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 1-9.
[4] WANG Zhi, CHEN Dong-hua, HE Yu-cheng. Research on beamforming design for multi-user full-duplex SWIPT systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(7): 115-120.
[5] ZHANG Li-jun, GUO Ming-le. On complete moment convergence of weighted sums for arrays of rowwise asymptotically almost negatively associated random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 42-49.
[6] XIONG Li-yan, XU Gui-qiao. The average error of linear tensor product multivariate polynomial interpolation based on Chebyshev nodes on the Brownian sheet measure [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 11-15.
[7] HUANG Ling-ling, ZHAO Kai. Boundedness of the parameterized Marcinkiewicz integral operators with variable kernels on weighted Campanato spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 1-5.
[8] FENG Guo-he, WANG Dan-di, LI Mei-chan. Text topic mining of archives research based on SVD [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(1): 95-100.
[9] DENG Long-juan, ZHU Dong-jin, SHEN Guang-jun. Power variation of weighted-fractional Brownian motion and application [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 19-26.
[10] TAN Chuang, GUO Ming-le, ZHU Dong-jin. Complete moment convergence of weighted sums of arrays of rowwise ND random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(06): 27-32.
[11] GOU Yin-xia, TAO Shuang-ping, DAI Hui-ping. Weighted estimates of fractional integral with rough kernel and its commutators on Herz-type Hardy Spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(07): 80-87.
[12] GUO Jing1, CHEN Xiang-en1, WANG Zhi-wen2. Irregular assignments of the union of several vertex-disjoint #br# paths with order n [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 18-25.
[13] PAN Yali, LI Chang-wen. Boundedness of commutators related to Marcinkiewicz integrals with #br# variable kernels on weighted weak Hardy spaces#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 84-89.
[14] XU Ri-li, GUO Ming-le*. Complete moment convergence of weighted sums of  arrays of rowwise ND random variables [J]. J4, 2013, 48(6): 9-13.
[15] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors [J]. J4, 2013, 48(1): 83-88.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd