= Matrix 2-norm
{title2=$\|A\|_2$}
= Spectral norm
{synonym}
The matrix 2-norm is the <operator norm> induced by the <Euclidean norm>:
$$
\|A\|_2=\sup_{x\ne0}\frac{\|Ax\|_2}{\|x\|_2}.
$$
It equals the largest <singular value> of $A$ and is invariant under multiplication by <orthogonal matrix>[orthogonal] or <unitary operator>[unitary] matrices.
The <matrix norm> induced by Euclidean vector norms is $\|A\|_2=\sup_{x\ne0}\|Ax\|_2/\|x\|_2$, equal to the largest singular value.
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