frobenius norm

So, I have been doing some reading... and have
encountered something that I am confused about...

I have read that if E is an outer product, E=uv*, then
||E||_2= (||u||_2)(||v||_2). (Where the * represents
the conjugate transpose, and ||x|| represents the norm).

So, my question is: is the same true for the
Frobenius norm? Ie: ||E||_F= (||u||_F)(||v||)_F)?
.

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