ON THE STRUCTURE AND GEOMETRY OF THE PRODUCT SINGULAR VALUE DECOMPOSITION

被引:7
|
作者
DEMOOR, BLR
机构
[1] B-3001 Leuven
关键词
D O I
10.1016/0024-3795(92)90290-Q
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The product singular value decomposition is a factorization of two matrices, which can be considered as a generalization of the ordinary singular value decomposition, at the same level of generality as the quotient (generalized) singular value decomposition. A constructive proof of the product singular value decomposition is provided, which exploits the close relation with a symmetric eigenvalue problem. Several interesting properties are established. The structure and the nonuniqueness properties of the so-called contragredient transformation, which appears as one of the factors in the product singular value decomposition, are investigated in detail. Finally, a geometrical interpretation of the structure is provided in terms of principal angles between subspaces.
引用
收藏
页码:95 / 136
页数:42
相关论文
共 50 条
  • [1] THE SINGULAR VALUE DECOMPOSITION IN PRODUCT FORM
    CUPPEN, JJM
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1983, 4 (02): : 216 - 222
  • [2] THE PRODUCT-PRODUCT SINGULAR VALUE DECOMPOSITION OF MATRIX TRIPLETS
    ZHA, HY
    [J]. BIT, 1991, 31 (04): : 711 - 726
  • [3] On the nonuniqueness of the factorization factors in the product singular value decomposition
    Chu, DL
    De Moor, B
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 314 (1-3) : 191 - 203
  • [4] COMPUTING THE SINGULAR VALUE DECOMPOSITION OF A PRODUCT OF 2 MATRICES
    HEATH, MT
    LAUB, AJ
    PAIGE, CC
    WARD, RC
    [J]. SIAM JOURNAL ON SCIENTIFIC AND STATISTICAL COMPUTING, 1986, 7 (04): : 1147 - 1159
  • [5] Geometry of curves in Rn from the local singular value decomposition
    Alvarez-Vizoso, J.
    Arn, Robert
    Kirby, Michael
    Peterson, Chris
    Draper, Bruce
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 571 : 180 - 202
  • [6] On Properties and Structure of the Analytic Singular Value Decomposition
    Weiss, Stephan
    Proudler, Ian K.
    Barbarino, Giovanni
    Pestana, Jennifer
    Mcwhirter, John G.
    [J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2024, 72 : 2260 - 2275
  • [7] Accurate computation of the product-induced singular value decomposition with applications
    Drmac, Z
    [J]. SIAM JOURNAL ON NUMERICAL ANALYSIS, 1998, 35 (05) : 1969 - 1994
  • [8] A randomized tensor singular value decomposition based on the t-product
    Zhang, Jiani
    Saibaba, Arvind K.
    Kilmer, Misha E.
    Aeron, Shuchin
    [J]. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 2018, 25 (05)
  • [9] UNITARY EQUIVALENCE IN AN INDEFINITE SCALAR PRODUCT - AN ANALOG OF SINGULAR-VALUE DECOMPOSITION
    BOLSHAKOV, Y
    REICHSTEIN, B
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1995, 222 : 155 - 226
  • [10] FAST SINGULAR VALUE THRESHOLDING WITHOUT SINGULAR VALUE DECOMPOSITION
    Cai, Jian-Feng
    Osher, Stanley
    [J]. METHODS AND APPLICATIONS OF ANALYSIS, 2013, 20 (04) : 335 - 352