Matrix 2-norm ($\Vert A{\Vert }_2$)

The matrix 2-norm is the operator norm induced by the Euclidean norm:It equals the largest singular value of $A$ and is invariant under multiplication by orthogonal or unitary matrices.

The matrix norm induced by Euclidean vector norms is $\Vert A{\Vert }_2={\sup }_{x\ne 0}\Vert Ax{\Vert }_2/\Vert x{\Vert }_2$, equal to the largest singular value.