Re: [線代] 一題考古題

看板Math作者Sfly (topos)時間14年前 (2012/02/15 16:31)推噓4(4推 0噓 2→)

留言6則, 4人參與討論串4/4 (看更多)

※ 引述《silentsecret ()》之銘言： : 若A、B為n*n實矩陣，AB=BA : 證明A、B有一共同的eigenvector : 請問大家了! over C, there exists some k that is an eigenvalue of A Let V=ker(A-kI) AB=BA => V is stable under B. So, as a morphism, we can consider the restriction B|V Again, there exists an eigenvector (in V) for B|V. Then we are done. PS.This implies that if A has n different eigenvalues,then B is diagonalizable. -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 76.94.119.209 ※ 編輯: Sfly 來自: 76.94.119.209 (02/15 16:32)

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jack0711

02/15 16:33, , 1^F

02/15 16:33, 1^F

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hjmeric

02/15 16:35, , 2^F

02/15 16:35, 2^F

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jack0711

02/15 16:39, , 3^F

02/15 16:39, 3^F