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Math Help - nonsingular linear map- help with some proof

  1. #1
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    nonsingular linear map- help with some proof

    There is a problem with an answer, however I don't understand why there is any need for the bolded part? Isn't it superfluous?
    Thanks in advance!
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  2. #2
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    Re: nonsingular linear map- help with some proof

    it's an "if and only if" proof.

    the "if part": if h preserves linear independence, h is non-singular. this is the part that is proved by the bold section. this is actually proved by proving the contra-positive: h is singular implies h takes SOME linearly independent set to a linearly dependent one.

    the linearly independent set they choose is S = {v}, where v is some non-zero element of the null space (which exists BECAUSE h is singular). this of course, maps to h(S) = {0W}, which is ALWAYS linearly dependent.

    you have to include BOTH implications in an if and only if proof, you can't leave one out.
    Thanks from jojo7777777
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  3. #3
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    Re: nonsingular linear map- help with some proof

    Thank you very much...!!!
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