[線代] 幾題eigenvalue問題

看板Math作者willyeh (fen)時間15年前 (2010/12/30 22:55)推噓1(1推 0噓 0→)

留言1則, 1人參與討論串1/2 (看更多)

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 麻煩幫解決這二題，謝謝。 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.117.193.14

推

Madroach

12/30 23:31, , 1^F

12/30 23:31, 1^F

‣ 返回看板[ Math ] 數學

‣ 更多 willyeh 的文章

文章代碼(AID): #1D79rNjO (Math)