Question: Show that for a fixed v R p the map T v such that T v ( x ) = v x is a real

Show that for a fixed vRp the map Tv such that Tv(x)=vx is a real valued linear map on Rp, i.e. belongs to the space L(Rp,R).

Now prove that the map on Rp given (v)=Tv is an isomorphism from Rp to L(Rp,R) if v is non-zero.

What would the matrix of (v) be (with respect to the standard bases of Rp and R)?

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