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Math Help - Need help proving norm equivalence theorem

  1. #1
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    Need help proving norm equivalence theorem

    For homework I need to prove these three equations and I am having trouble knowing where to start. Here is the problem:

    Given A in R(mxn), show that:

    1. ||A||2 <= ||A||F <= sqrt(n) * ||A||2
    2. (1 / sqrt(n)) * ||A||inf <= ||A||2 <= sqrt(m) * ||A||inf
    3. (1 / sqrt(m)) * ||A||1 <= ||A||2 <= sqrt(n) * ||A||1

    I assume ||A||2 = spectral radius = the max eigenvalue and ||A||F = sum(sum(A(i,j))) i = 1..m, j=1..n. I just dont even know where to start really.
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  2. #2
    Super Member girdav's Avatar
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    Re: Need help proving norm equivalence theorem

    Are you sure that the norms ||\cdot||_i, i=1,2,\infty are not the matrix norms corresponding to theses norms on \Bbb R^n,\Bbb R^m.
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