[線代] inner product and Kernel

看板Math作者 (asdc20)時間13年前 (2013/02/05 19:54), 編輯推噓0(0推 0噓 3→)
留言3則, 2人參與, 最新討論串1/1
Inner product: Consider the set of all integrable functions on [a,b]. Determine whether <x,y>=x(a)y(a) is a suitable inner product. Kernel: Consider the integral operator L on C([a,b];R) defind by Lx=∫K(γ,t)x(γ)dγ (integral form a to b) where K is is a given continuous function, called Kernel of L. Show that L is a linear operator. 先謝謝各位 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 129.7.255.32 ※ 編輯: asdc20 來自: 129.7.255.32 (02/05 19:55)
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02/05 20:11, , 1F
1. No, an inner product should be p.d.
02/05 20:11, 1F
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02/05 20:14, , 2F
2. L is linear, bounded, and compact. It is easy.
02/05 20:14, 2F
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02/05 21:10, , 3F
因為積分線性運算
02/05 21:10, 3F
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