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Math Help - Bases and Linear Maps

  1. #1
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    Bases and Linear Maps

    Hi, Quick question:


    If I know that T:V -> W is injective and B is a basis of V, how can i use that to show that T(B) is a basis of W?

    Thanks
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  2. #2
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    Quote Originally Posted by dr4g0n9 View Post
    Hi, Quick question:


    If I know that T:V -> W is injective and B is a basis of V, how can i use that to show that T(B) is a basis of W?

    Thanks

    You can't because it isn't true: T: \mathbb{R}\rightarrow \mathbb{R}^2\,,\,\,T(r)=(r,0) is injective but not onto and thus no basis of the definition set can be mapped to a basis of the image set.

    What is true is that if T is injective then the image of a basis is a lin. indep. set.

    Tonio
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