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Math Help - kernal

  1. #1
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    kernal

    let V and W be a finite dimensional vector space and f:V-->W. prove that the ker(f) is finite dimensional.

    my workings:

    since the dimV is finite dim, let dimV= n, n is a real number

    dim V= nullity f + rank f = n

    dim(ker(f)) is less than or equal to n, thus it is finite dimensional.

    this seems like a rather straightforward way of proofing..not sure if it is that simple..
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  2. #2
    Member HappyJoe's Avatar
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    Your argument is perfectly fine.

    Another way: It also follows from the more general result that any subspace of a finite-dimensional vector space is finite-dimensional.
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