Infimum of a Matrix Norm of A Induced by an Absolute Vector Norm

被引：0

作者：

Friedland, Shmuel ^{[1
]}

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS | 2022年 / 46卷 / 06期

关键词：

Absolute norm; Matrix norm; Nonnegative matrices; Spectral radius;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We characterize the infimum of a matrix norm of a square matrix A induced by an absolute norm, over the fields of real and complex numbers. Usually this infimum is greater than the spectral radius of A. If A is sign equivalent to a nonnegative matrix B then this infimum is the spectral radius of B.

引用

页码：713 / 720

页数：8

共 50 条

[1] NORM INFIMUM FUNCTION
APPLING, WDL
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (01): : 102 - &
[2] CONTINUITY AND SUBDIVISION NORM INFIMUM FUNCTION
APPLING, WDL
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 17 (02): : 438 - &
[3] IS THE FROBENIUS MATRIX NORM INDUCED
CHELLABOINA, VS
HADDAD, WM
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1995, 40 (12) : 2137 - 2139
[4] Comments on "Is the Frobenius matrix norm induced?"
Djouadi, SM
IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (03) : 518 - 519
[5] On the Matrix Norm Subordinate to the Holder Norm
Albrecht, J.
Klein, P. P.
ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 1999, 18 (02): : 175 - 182
[6] Absolute Logarithmic Norm
Perov, A. I.
Kostrub, I. D.
Kleshchina, O. I.
Dikarev, E. E.
RUSSIAN MATHEMATICS, 2018, 62 (04) : 60 - 73
[7] NORM OF A MATRIX
DEUTSCH, E
AMERICAN MATHEMATICAL MONTHLY, 1980, 87 (10): : 831 - 831
[8] ON A MATRIX NORM
DAZORD, J
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1991, 312 (08): : 597 - 600
[9] ON THE NORM OF A MATRIX
BOWKER, AH
ANNALS OF MATHEMATICAL STATISTICS, 1947, 18 (02): : 285 - 288
[10] VECTOR NORM INEQUALITY
KLAMKIN, MS
AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (08): : 829 - 830

← 1 2 3 4 5 →