CAJ | 학술논문

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 (S)m (A) of m-involutions that anti-commute with a matrix A ∈ Cn×n.