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Squaring a linear transformation

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Homework Statement


Prove that T[itex]^{2}[/itex] is a linear transformation if T is linear (from R[itex]^{3}[/itex] to R[itex]^{3}[/itex].


So I understand when a transformation is considered linear, but I don't understand what squaring a transformation does. I don't think it means squaring the result of the transformation but I'm not sure how else to think of it. Or maybe I'm forgetting some convenient property that would make this proof short and sweet. Any help is very much appreciated!
 

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  • #2
Ray Vickson
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Homework Statement


Prove that T[itex]^{2}[/itex] is a linear transformation if T is linear (from R[itex]^{3}[/itex] to R[itex]^{3}[/itex].


So I understand when a transformation is considered linear, but I don't understand what squaring a transformation does. I don't think it means squaring the result of the transformation but I'm not sure how else to think of it. Or maybe I'm forgetting some convenient property that would make this proof short and sweet. Any help is very much appreciated!
T^2(x) = T(T(x)).

RGV
 
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