Schur complements and state space realizations

被引：18
|
作者：
Bart, H
Gohberg, I
Kaashoek, MA
Ran, ACM
机构：
[1] Erasmus Univ, Inst Econometr, NL-3000 DR Rotterdam, Netherlands
[2] Tel Aviv Univ, Sch Math Sci, Raymond & Beverly Sackler Fac Exact Sci, Ramat Aviv, Israel
[3] Vrije Univ Amsterdam, Dept Math, FEW, NL-1081 HV Amsterdam, Netherlands
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 399卷
关键词：
equivalence; extension; factorization; realization; Schur complement; transfer function;
D O I：
10.1016/j.laa.2004.10.027
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Motivated by state space realizations of transfer functions from system theory, a number of operations on Schur complements are introduced and studied. These operations are equivalence, extension, multiplication, inversion, and factorization. Together they form an algebraic framework which is of independent interest, and also useful in solving problems in analysis. (c) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：203 / 224
页数：22
相关论文
共 50 条
  • [1] Schur complements of selfadjoint Krein space operators
    Contino, Maximiliano
    Maestripieri, Alejandra
    Marcantognini, Stefania
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2019, 581 : 214 - 246
  • [2] GENERALIZED SCHUR COMPLEMENTS
    ANDO, T
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1979, 27 (OCT) : 173 - 186
  • [3] SCHUR COMPLEMENTS AND STATISTICS
    OUELLETTE, DV
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1981, 36 (MAR) : 187 - 295
  • [4] On the embedding of state space realizations
    Yves Genin
    Antoine Vandendorpe
    Mathematics of Control, Signals, and Systems, 2007, 19 : 123 - 149
  • [5] On the embedding of state space realizations
    Genin, Yves
    Vandendorpe, Antoine
    MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS, 2007, 19 (02) : 123 - 149
  • [6] COMPLEMENTARY SCHUR COMPLEMENTS
    BART, H
    TSEKANOVSKII, VE
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1994, 198 : 651 - 658
  • [7] Complementary schur complements
    Bart, H.
    Tsekanovskii, V.E.
    Linear Algebra and Its Applications, 1994, 197-98
  • [8] Schur complements and Banachiewicz-Schur forms
    Tian, YG
    Takane, Y
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2005, 13 : 405 - 418
  • [9] Some properties of Schur complements and diagonal-Schur complements of diagonally dominant matrices
    Liu, Jianzhou
    Li, Jicheng
    Huang, Zhuohong
    Kong, Xu
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2008, 428 (04) : 1009 - 1030
  • [10] 6 GENERALIZED SCHUR COMPLEMENTS
    BUTLER, CA
    MORLEY, TD
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1988, 106 : 259 - 269
12345