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Dimension of subspace

  1. Jun 15, 2005 #1
    Hi,
    I'm just learning for my linear algebra exam and I wonder if somebody could give me an example of a nontrivial subspace which has as many dimensions as the original space.
    Thanks a lot
     
  2. jcsd
  3. Jun 15, 2005 #2

    HallsofIvy

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    What do you mean by "nontrivial". I would call a subspace nontrivial as long as it was not just the 0 vector. If that's the case then just take any vectors space V with V as the subspace.

    Another possibility, a lot more non-trivial would be an infinite dimensional vector space with an infinite dimensional subspace.
    The vector space of all polynomials with subspace the space of all even polynomials comes to mind.
     
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