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# 線代norm証明一題

証明

|| x||_∞ = lim (n→∞) || x||_p

x=(x_1,x_2,...,x_n) in C^n

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Update:

sorry

|| x||_∞ = lim (p→∞) || x||_p

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### 1 Answer

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- mathmanliuLv 71 decade agoFavorite Answer
題目有錯字!

2009-03-23 22:43:44 補充：

設 M= max{ |x1|, |x2|, ..., |xn| } = || x ||_∞

M <= || x ||_p <= (nM^p)^(1/p) = n^(1/p) * M

=> M <= lim(p->∞) || x ||_p <= lim(p->∞) [n^(1/p)M]

左右兩邊極限值均為M

=>(Squeeze) lim(p->∞) || x||_p = M = || x||_∞

得證

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