Genre
- Journal Article
The following questions are studied: Under what conditions does the existence of a (nonzero) fixed point for every member of a semigroup of matrices imply a common fixed point for the entire semigroup? What is the smallest number k such that the existence of a common fixed point for every k members of a semigroup implies the same for the semigroup? If every member has a fixed space of dimension at least k: What is the best that can be said about the common fixed space? We also consider analogs of these questions with general eigenspaces replacing fixed spaces.
Univ Ljubljana, Dept Math, Ljubljana 1000, Slovenia. Natl Univ Ireland Univ Coll Dublin, Dept Math Sci, Dublin 4, Ireland. Univ Prince Edward Isl, Dept Math & Comp Sci, Charlottetown, PE C1A 4P3, Canada. Technion Israel Inst Technol, Dept Math, (TRUNCATED)
ABINGDON; 4 PARK SQUARE, MILTON PARK, ABINGDON OX14 4RN, OXON, ENGLAND
TAYLOR & FRANCIS LTD
PT: J; CR: BENSON RV, 1966, EUCLIDEAN GEOMETRY C BERNIK J, UNPUB SMIGROUPS MATR BERNIK J, 2003, SEMIGROUP FORUM, V67, P271 CURTIS CW, 1962, REPRESENTATION THEOR GURALNICK RM, 1980, LINEAR MULTILINEAR A, V9, P133 PASSMAN DS, 1968, PERMUTATION GROUPS RADJAVI H, 2000, SIMULTANEOUS TRIANGU; NR: 7; TC: 0; J9: LINEAR MULTILINEAR ALGEBRA; PG: 10; GA: 921ES
Source type: Electronic(1)
Language
- English
Subjects
- reducibility
- groups and semigroups of matrices
- fixed points
- common eigenvectors
- Mathematics