※ 引述《ILzi ( 并不好笑 )》之铭言： : nxn : 设A€F ,试证：dim(span{I,A,A^2,...})≦n : 麻烦各位了 : 谢谢 det (A-A)= Σ(Iλi-A) = Σai*A^i = 0 Σai*A^(i+n)=0 for any n € Ν .............................(1) [I,A,A^2,...]x=0 has the solution of x=(a0 a1 .......an) ....(2) (2) ∴ dim (span[I,A,A^2,...A^n]) ≦ n (=n when ai=0 for all i) (1)and(2) ∴ any A^(n+1) is linear combinition of [A,A^2,....A^n] =>dim (span[I,A,A^2,...]) ≦ n --

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