$\|A\|_2 = \sup_{\|x\|_2 = 1} \|Ax\|_2 = \sup_{\|x\|_2 = 1} \|Ax\|_F$
since A is a matrix and x is a vector, then $Ax$ is a vector. And we have that $\|x\|_2 = \|x\|_F$, right?
2026-03-26 20:38:30.1774557510
Relation between 2-norm and F-norm
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if you mean by $F$ the Frobenius norm then yes $\vert \vert x\vert \vert$$_F$$=$$\vert \vert x\vert \vert$$_2$