u**x
发帖数: 45 | 1 I learned the concept of norm long time back, but have been coming across it
frequently. So let me try to recite what I learned.
矩阵范数的定义是与矢量空间的内积和范数的相联系的
矢量空间的范数的定义是: ||||: X->R s.t.
1) ||x||>=0, for any x b.t. X and ||x||=0 iff x=0
2) ||ax||=|a|||x||, for any vector x b.t. X , and scalar a b.t. C
3) ||x+y||=||x||+||y||, for any x, y b.t. X.
当矢量空间, X=C^n 时, 复矢量的欧氏范数可定义作 ||x||2=(x,x)^(1/2)
更广义的, n 维复矢量的Holder范数的定义是
||x||p=(sigma(|xi|^p, {i,1,n}))^(1/p)
其中P为2时, 它就是欧氏范数. 另外p=1, p=inf也是常用范数. 通常它们 |
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