Re: [理工] [線代]-矩陣表示

[elps ( )]

※ 引述《yesa315 (XD)》之銘言：
: A matrix representation of a linear operator on M : m x n ,the set of all
: m x n matrices, is an m x n matrix
: 此題為FALSE 但我看不太懂題目再說啥!?
意思是取 linear operator T: M -> M, where M:mxn

因為一個 M:mxn 的矩陣是屬於一個維度為 m*n 的向量空間

所以 T 的矩陣表示法應該要是一個 (m*n)x(m*n) 的矩陣
:                               n                     n
: If T is a linear operator on R  , B is a basis for R , C is the matrix
: whose columns are the vectors in B and A is the standard matrix of T ,
:                   -1
: then [T]   = C A C
:         B
: 此題為FALSE 但 C is the matrix whose columns are the vectors in B
: 這句話不太懂
: 請高手指導  謝謝
假設 S 為 standard basis of R^n,


                     S          S
這裡的 C 其實就是 [I]  , A = [T]
                     B          S


              B    S    S     -1
所以 [T] = [I]  [T]  [I]   = C  A C
        B     S    S    B

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