The Rational Proof Of The Theorem Of Double Centre Of Matrices

If F is a field, A is a matrix of degree n in F,we mark and call C(A) is the centre of A. The theorem of double centre of matrices is a fundamental conclusion about it: It has been proved in some literatures by using the Jordan standard form. In this way we naturally suppose F is large enough, that is to say the characteristic polynomial f(λ)=|λE-A|of A is split in F. In this paper we give the proof of the important theorem from the perspective of rational standard form. F is certainly arbitrary. Thus we could more naturally understand the theorem of double centre of matrices.