Let T:R^3-->R^3 be a linear map such that T(e1)=(0,0,0) , T(e2)=e3 , T(e3)=(0,0,0).prove that T is nilpotent linear map and R^3 is not T-cyclic.

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- December 9th 2009, 12:40 AMmath.djT-cyclic
Let T:R^3-->R^3 be a linear map such that T(e1)=(0,0,0) , T(e2)=e3 , T(e3)=(0,0,0).prove that T is nilpotent linear map and R^3 is not T-cyclic.

- December 9th 2009, 07:16 AMHallsofIvy
- December 10th 2009, 03:33 AMmath.dj
Nilpotent: A linear map T:V--.V is said to be nilpotent if T^m=0, for some m in N.

T-Cyclic:Given a nilpotent linear map T:V-->V (dim(V)=n )then V is said to be t-Cyclic if there exist a v in V such that {v,T(v),...,Tn-1(v)} is a basis of V..