SINGULAR-VALUES, DOUBLY STOCHASTIC MATRICES, AND APPLICATIONS

被引:26
作者
ELSNER, L [1 ]
FRIEDLAND, S [1 ]
机构
[1] UNIV ILLINOIS,DEPT MATH STAT & COMP SCI,CHICAGO,IL 60607
关键词
D O I
10.1016/0024-3795(95)00111-4
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The Hadamard square of any square matrix A is bounded above and below by some doubly stochastic matrices times the square of the largest and the smallest singular values of A. Applications to graphs, permanents, and eigenvalue perturbations are discussed.
引用
收藏
页码:161 / 169
页数:9
相关论文
共 12 条
  • [1] Cruse, A proof of Fulkerson's characterization of permutation matrices, Linear Algebra Appl., 12, pp. 21-28, (1975)
  • [2] Egorichev, The solution of the van der Waerden problem for permanents, Dokl. Akad. Nauk SSSR, 258, pp. 1041-1044, (1981)
  • [3] Elsner, A note on the Hoffman-Wielandt theorem, Linear Algebra Appl., 182, pp. 235-237, (1993)
  • [4] Falikman, A proof of van der Waerden's conjecture on the permanents of a doubly stochastic matrix, Mat. Zametki, 29, pp. 931-938, (1981)
  • [5] Friedland, A proof of a generalized van der Waerden conjecture on permanents, Linear and Multilinear Algebra, 11, pp. 107-120, (1982)
  • [6] Friedland, Every 7-regular digraph contains an even cycle, J. Combin. Theory Ser. B, 46, pp. 249-252, (1989)
  • [7] Friedland, Li, Schneider, Additive decompositions of nonnegative matrices with applications to permanents and scaling, Linear and Multilinear Algebra, 23, pp. 63-78, (1988)
  • [8] Fulkerson, The maximum number of disjoint permutations contained in a matrix of zeros and ones, Canadian Journal of Mathematics, 16, pp. 729-735, (1964)
  • [9] Marcus, Minc, A Survey of Matrix Theory and Matrix Inequalities, (1964)
  • [10] Stewart, Sun, Matrix Perturbation Theory, (1990)