### Definition of Two-norm

1. Noun. Mathematical measure of length given by "the square root of the squares." Denoted by $||\cdot||_2$, the two-norm of a vector is $||\vec v||_2=\sqrt\left\{a_1^2+a_2^2+\cdots+a_n^2\right\}$. The two norm of an $m\times m$ matrix $A$ is defined by $\max_\left\{\vec v\neq\vec 0\right\}\frac\left\{||A\vec v||_2\right\}\left\{||\vec v||_2\right\}$ where $\vec v$ is an m-dimensional vector that is not the zero vector. ¹

¹ Source: wiktionary.com

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### Lexicographical Neighbors of Two-norm

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