[理工] [線代]-Linear transformation

[gn00618777 (123)]

        n      n
Let T: R ---> R  be a linear transformation. Prove that,if
                                    n
T(T(x))=T(x)+T(x)+3x,for all x 屬於R , Then T is one to one
            n       n
mapping of R  into R

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→ gn00618777:冏" 好像沒啥人裡我
推 sorrel20567:若linear transformation  且T(0)=>0   則1-1 trivial
→ sorrel20567:令T(X)=0  則T(T(X))= T(0)=0+0+3*0=0
→ sorrel20567:T(0)送到0   所以T為1-1