数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (2): 631-644.doi: 10.1016/S0252-9602(12)60044-7
Mark Yasuda
Mark Yasuda
摘要:
We define an m-involution to be a matrix K ∈ Cn×n for which Km = I. In this article, we investigate the class Sm (A) of m-involutions that commute with a diagonalizable matrix A ∈ Cn×n. A number of basic properties of Sm (A) and its related subclass Sm (A, X) are given, where X is an eigenvector matrix of A. Among them, Sm (A) is shown to have a torsion group structure under matrix multiplication if A has distinct eigenvalues and has non-denumerable cardinality otherwise. The constructive definition of Sm (A, X) allows one to generate all m-involutions commuting with a matrix with distinct eigenvalues. Some related results are also given for the class ˜ Sm (A) of m-involutions that anti-commute with a matrix A ∈ Cn×n.
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