Compact Abelian Semigroups of Matrices
Yongwen Zhu · Journal of Mathematical Research and Exposition · 2007
The eigenvalues of the matrices in a compact abelian[Hermite]matrix semigroup are de- termined 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±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.