Compact Abelian Semigroups of Matrices
Received:December 26, 2005  Revised:July 02, 2006
Key Words: matrix semigroups   abelian semigroups   simple semigroups   compact   Hermite matrices.  
Fund Project:the National Natural Science Foundation of China (10301004).
Author NameAffiliation
ZHU Yong-wen School of Mathematics and Information Science, Yantai University, Shandong 264005, China 
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Abstract:
      The eigenvalues of the matrices in a compact abelian [Hermite] matrix semigroup are determined by means of the simultaneous diagonalization or trianglization of matrices. It is shown that the eigenvalues of each matrix of a compact semigroup consisting of invertible Hermite matrices are $\pm 1$, that a simple semigroup of Hermite matrices is similar to a semigroup of diagonal matrices, and that the spectrum radium of a compact commutative semigroup of matrices is less than or equal to $1$, etc.
Citation:
DOI:10.3770/j.issn:1000-341X.2007.03.020
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