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asked in 科學數學 · 1 decade ago

線代判斷兩矩陣similiar的問題

如果已知兩矩陣A,B的determine , trace , characteristic polynomial , minimal polynomial都相同 如果A,B都不可對角化 那要怎麼判斷A,B是否similiar,是要用jordan form來看嗎??

Update:

那如果這兩個矩陣在R上 characteristic polynomial 不split 找不到jordan form呢??

Update 2:

那這種情況要怎麼判斷是否similiar

1 Answer

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  • 1 decade ago
    Favorite Answer

    假設兩矩陣A,B are similar,則A,B的determine,trace,characteristic polynomial,minimal polynomial都相等,這是必要條件,不是充分條件因此要判斷A,B是否similar,唯一的方法就是利用JA=JB if and only if A~B的方法去判斷,其中JA為A的jordan form,依此類推

    2006-10-14 22:16:05 補充:

    如果在R上不能split,當然就不存在該矩陣的jardan form

    2006-10-15 17:56:50 補充:

    這種情況當然就無法判定是否similar,因為它們的characterastic polynomial is not defined

    Source(s): 自己
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