I study about random projection and i m really confuse about the relationship between Frobenius norm and singular values. The book say that the $||M||_f^2 $ and $\sigma$ had a correlation.
I found this
but i really dont take the meaning. For me if
$||M||_f= \sqrt \sum _i σ_i^2$
the square is just
$||M||_f^2 = \sum _i σ_i^2$
My book say that the relationship is between all singular value $\sigma_1 (M), \sigma_2(M)... $
Someone can help me on this?