[線代] 台大某年
許多題目都毫無頭緒
希望大家可以繼續不厭其煩地幫助我QAQ
1. V is a vector space of function over |R. Show that {sin^n(x)} is a linear
independent set of V, n=0,1,2...
無限獨立集是說拿任一數目出來都是獨立嗎?
inf
還是是要用令 0=sum a_n*sin^{n}(x)這樣嗎?
0
還是有特別的解法?(我原本以為是內積)
2.Let V be a vector space over a field F and T is a linear transform on V
such that for all v in V, there exists a λ_v in F such that T(v)=λ_v*v.
Show that there is a λ in F such that T(v)=λv for all v in V.
似乎是無限維度才對,原本以為 p_T(x)=det(T-xI) 恆等於0(因為全部的v都是eigenvalue
後來想想也可能因為無限維度所以我的想法是錯的
這題可以直接開圖找出那個λ嗎?
3.Let F be a field and A_1,...A_{n^2} be a basis of M_{n*n}(F).Show that for
any set c_1,...c_{n^2} in F there exists a B in M_{n*n}(F) such that
tr(A_iB)=c_i for all i=1,...n^2
原本想用數學歸納法試試看
可是找不到一個理由讓滿足前n^2-1的那個B會讓tr(A_{n^2}B)=c_{n^2}
感謝大家QAQ
怎麼這麼快就要推甄了(崩潰
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◆ From: 111.240.210.143
※ 編輯: jacky7987 來自: 111.240.210.143 (09/12 03:43)
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