User:Myturn~enwikibooks

Time killer

http://www.c6.org/archive/tony/killer.jpg

''$$Let A be the matrix of T. Then A^k is the matrix of T^k, and$$

$$        det(A^k - e^kI)$$

$$      = det((A - eI)(A^(k-1) + eA^(k-2) + ... + e^(k-1)))$$

$$      = det(A - eI) det(A^(k-1) + eA^(k-2) + ... + e^(k-1))$$

$$    det(A - eI) = 0 since e is an eigenvalue of T, that is,$$

$$    det(A^k - e^kI) = 0, that is, e^k is an eigenvalue of T^k.$$''

HI. 我是 myturn
--Myturn 06:38, 19 Sep 2004 (UTC)