作者willyeh (fen)
看板Math
标题[线代] 几题eigenvalue问题
时间Thu Dec 30 22:55:16 2010
1
If P is the matrix thar projects R^n onto a subspace S, explain why every
vector in S is an eigenvector, and so is every vector in complement of S.
What are the eigenvalues?(Note the connection to P^2=P, which means that
eigenvalue^2=eigenvalue)
2
(a)Show that the matrix differential equation dX/dt=AX+XB has the solution
X(t)=e^At X(0) e^Bt
(b)Prove that the solutions of dX/dt=AX-XA keep the same eigenvalues for all
time
麻烦帮解决这二题，谢谢。
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1F：推 Madroach :T是projection operator等价T=TT 12/30 23:31