RANK OF LINEAR AND QUADRATIC COMBINATIONS OF MATRICES

被引：0
|
作者：
Johnson, Ch R. [1 ]
Pena, J. M. [2 ]
Szulc, T. [3 ]
机构：
[1] Coll William & Mary, Dept Math, Williamsburg, VA 23185 USA
[2] Univ Zaragoza, Dept Matemat Aplicada, E-50009 Zaragoza, Spain
[3] Adam Mickiewicz Univ, Fac Math & Comp Sci, Umultowska 87, PL-61614 Poznan, Poland
来源：
ELECTRONIC JOURNAL OF LINEAR ALGEBRA | 2020年 / 36卷
关键词：
Rank; Full rank factorization; Linear combinations of matrices; Convex combinations; Quadratic combinations; P-matrices;
D O I：
10.13001/ela.2020.4949
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, the rank of some combinations of matrices is analysed. In particular, the rank of all matrices on the line joining two rank 1 matrices is characterized, and the rank of convex combinations of two matrices and quadratic combinations of three matrices is studied. Presented results concern the problem of robustness of rank under certain kinds of perturbations of a matrix.
引用
收藏
页码：169 / 176
页数：8
相关论文
共 50 条
  • [41] Solving Complex Quadratic Systems With Full-Rank Random Matrices
    Huang, Shuai
    Gupta, Sidharth
    Dokmanic, Ivan
    IEEE TRANSACTIONS ON SIGNAL PROCESSING, 2020, 68 : 4782 - 4796
  • [42] DETERMINATION OF WEIGHTING MATRICES OF A LINEAR-QUADRATIC REGULATOR
    LUO, J
    LAN, CE
    JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 1995, 18 (06) : 1462 - 1463
  • [43] Linear operators that preserve Boolean rank of Boolean matrices
    LeRoy B. Beasley
    Seok-Zun Song
    Czechoslovak Mathematical Journal, 2013, 63 : 435 - 440
  • [44] FACTORING SPECTRAL MATRICES IN LINEAR-QUADRATIC MODELS
    BALL, JA
    TAUB, B
    ECONOMICS LETTERS, 1991, 35 (01) : 39 - 44
  • [45] Linear maps preserving rank of tensor products of matrices
    Zheng, Baodong
    Xu, Jinli
    Fosner, Ajda
    LINEAR & MULTILINEAR ALGEBRA, 2015, 63 (02): : 366 - 376
  • [46] LINEAR TRANSFORMATIONS PRESERVING SYMMETRIC RANK ONE MATRICES
    WATERHOUSE, WC
    JOURNAL OF ALGEBRA, 1989, 125 (02) : 502 - 518
  • [47] Real root finding for low rank linear matrices
    Didier Henrion
    Simone Naldi
    Mohab Safey El Din
    Applicable Algebra in Engineering, Communication and Computing, 2020, 31 : 101 - 133
  • [48] LINEAR OPERATORS THAT PRESERVE BOOLEAN RANK OF BOOLEAN MATRICES
    Beasley, LeRoy B.
    Song, Seok-Zun
    CZECHOSLOVAK MATHEMATICAL JOURNAL, 2013, 63 (02) : 435 - 440
  • [49] Real root finding for low rank linear matrices
    Henrion, Didier
    Naldi, Simone
    El Din, Mohab Safey
    APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2020, 31 (02) : 101 - 133
  • [50] Linear spaces of matrices of constant rank and instanton bundles
    Boralevi, Ada
    Faenzi, Daniele
    Mezzetti, Emilia
    ADVANCES IN MATHEMATICS, 2013, 248 : 895 - 920
12345