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Math Help - A linear which is not injective?

  1. #1
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    A linear which is not injective?

    Hi,

    exist a special case, where we have a map which is completly linear that is not injective?

    greetings

    p.s.

    I heard that injective in english is also translated to "one-to-one" Is this correct?
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  2. #2
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    Hi.
    What do you mean by completely linear?
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  3. #3
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    That there is no power higher than one.

    greetings
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  4. #4
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    The zero map is a linear map, and it is not injective!

    In the particular case of linear maps from \mathbb{R} to \mathbb{R}, a linear map is injective (and even bijective) iff it is a non constant map.

    In a more general case, linear map between two vector spaces can be non injective without being a constant map, for exemple
    x,y)\mapsto (x+y,0)" alt="f:\mathbb{R}^{2}\rightarrow \mathbb{R}^{2}x,y)\mapsto (x+y,0)" />

    p.s. Yes, one-to-one means injective.
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