a Department of Basic Sciences, Xiangtan Polytechnic University, Xiangtan, P. R. China
Abstract:
Let Rbe a finite dimensional central simple algebra over a field FA be any n× n matrix over R. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomial qA(λ) of A over F. By using qA(λ), this paper discusses the structure of right (left) eigenvalues set of A, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix.