Nilpotent matrix－xvnjcke的部落格

標題:

Nilpotent matrix

發問:

Let A and B be nilpotent 3x3 matrix stch that AB=BA, show that AB and A+B are nilpotent.

最佳解答:

AB(A + B) = ABA + ABB = A(AB) + (BA)B = A(AB) + B(AB) = (A + B)(AB) Hence AB and A + B are nilpotent. 2010-03-29 10:03:53 補充： Suppose that A^m and B^n = 0, where m and n are positive integers. Then, in case m > n: (AB)^m = (AB)(AB)...(AB) = A(BA)B(AB)...(AB) = A(AB)B(AB)...(AB) = A^2B^2 (AB)...(AB) . . = A^m B^m = 0 Similar approach for m = n and m
其他解答:

nilpotent不是commutative