# Math Help - Need help proving norm equivalence theorem

1. ## 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.

2. ## 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 $\Bbb R^n,\Bbb R^m$.