Range of a 4×5 matrix via its SVD
Returning to this example, the Frobenius norm is the square root of the sum of the squares of the elements, and is equal to
![\[ \|A\|_F=\sqrt{\sigma_1^2+\sigma_2^2+\sigma_3^2}=5.4772. \]](https://pressbooks.pub/app/uploads/quicklatex/quicklatex.com-39666d259b7ed595f58affda72b782c5_l3.png "Rendered by QuickLaTeX.com")
The largest singular value norm is simply 
. Thus, the Euclidean norm of the output 
cannot exceed four times that of the input 
.
