THE SPECTRAL NORM OF A NONNEGATIVE MATRIX

被引：39

作者：

MATHIAS, R ^{[1
]}

机构：

[1] JOHNS HOPKINS UNIV,DEPT MATH SCI,BALTIMORE,MD 21218

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 1990年 / 139卷

关键词：

D O I：

10.1016/0024-3795(90)90403-Y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a matrix A=[aij], define {norm of matrix}A{norm of matrix}=[{norm of matrix}aij{norm of matrix}]. Let {triple vertical-rule fence} · {triple vertical-rule fence}2 denote the spectral norm. We show that for any matrix A {triple vertical-rule fence}{norm of matrix}A{norm of matrix}{triple vertical-rule fence}2=min{r1(B)c1(C):B{ring operator}C=A} and show that under mild conditions the minimizers in (1) are essentially unique and are related to the left and right singular vectors of A in a simple way. We also show that {triple vertical-rule fence}A{triple vertical-rule fence}2≤{triple vertical-rule fence}{norm of matrix}A{norm of matrix}{triple vertical-rule fence}2 and determine the case of equality. © 1990.

引用

页码：269 / 284

页数：16

共 11 条

[1]

Golub G.H., 1983, MATRIX COMPUTATIONS

[2] A SURVEY OF CONDITION NUMBER ESTIMATION FOR TRIANGULAR MATRICES [J].

HIGHAM, NJ .

SIAM REVIEW, 1987, 29 (04) :575-596

[3]

Horn R.A, 2012, MATRIX ANAL, V2nd ed.

[4]

HORN RA, 1989, 485 J HOPK U DEP MAT

[5]

HORN RA, 1989, 514 J HOPK U DEP MAT

[6]

Minc H., 1988, NONNEGATIVE MATRICES

[7]

PANG JS, IN PRESS MATH OPER R

[8]

PAULSEN V. I, 1986, COMPLETELY BOUNDED M

[9]

Schur J., 1911, J REINE ANGEW MATH, V140, P1, DOI [DOI 10.1515/CRLL.1911.140.1, 10.1515/crll.1911.140.1]

[10]

STOER J, 1970, CONVEXITY OPTIMIZATI, V1

← 1 2 →