ON THE LENGTHS OF IRREDUCIBLE PAIRS OF COMPLEX MATRICES

被引：14

作者：

Longstaff, W. E. ^{[1
]}

Rosenthal, Peter ^{[2
]}

机构：

[1] Univ Western Australia, Sch Math & Stat, Crawley, WA 6009, Australia

[2] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 11期

关键词：

Length; words; REPRESENTATIONS; THEOREM; SIZE;

D O I：

10.1090/S0002-9939-2011-11149-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The length of a pair of matrices is the smallest integer l such that words in the matrices with at most l factors span the unital algebra generated by the pair. Upper bounds for lengths have been much studied. If B is a rank one n x n (complex) matrix, the length of the irreducible pair {A, B} is 2n - 2 and the subwords of A(n-1)BA(n-2) form a basis for M-n(C). New examples are given of irreducible pairs of n x n matrices of length n. There exists an irreducible pair of 5 x 5 matrices of length 4. We begin the study of determining lower bounds for lengths.

引用

页码：3769 / 3777

页数：9

共 9 条

[1] INVARIANT SUBSPACE LATTICE OF A LINEAR TRANSFORMATION [J].

BRICKMAN, L ;

FILLMORE, PA .

CANADIAN JOURNAL OF MATHEMATICS, 1967, 19 (04) :810-&

[2] Lengths of finite dimensional representations of PBW algebras [J].

Constantine, D ;

Darnall, M .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 395 :175-181

[3]

Freedman A, 1997, PAC J MATH, P159

[4] ON THE LENGTHS OF PAIRS OF COMPLEX MATRICES OF SIZE SIX [J].

Lambrou, M. S. ;

Longstaff, W. E. .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2009, 80 (02) :177-201

[5] On the lengths of pairs of complex matrices of size at most five [J].

Longstaff, W. E. ;

Niemeyer, A. C. ;

Panaia, Oreste .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2006, 73 (03) :461-472

[6] Burnside's theorem: irreducible pairs of transformations [J].

Longstaff, WE .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2004, 382 :247-269

[7] An upper bound for the length of a finite-dimensional algebra [J].

Pappacena, CJ .

JOURNAL OF ALGEBRA, 1997, 197 (02) :535-545

[8]

Paz A., 1984, Linear Multilinear Algebra, V15, P161, DOI [/10.1080/03081088408817585, DOI 10.1080/03081088408817585, 10.1080/03081088408817585]

[9]

RADJAVI H, 1970, J LONDON MATH SOC, V2, P557

← 1 →