What is the meaning of Two-norm?

A measure of length given by "the square root of the squares." Denoted by ${\displaystyle ||\cdot ||_{2}}$, the two-norm of a vector ${\displaystyle {\vec {v}}=<a_{1},a_{2},\ldots ,a_{n}>}$ is ${\displaystyle ||{\vec {v}}||_{2}={\sqrt {a_{1}^{2}+a_{2}^{2}+\cdots +a_{n}^{2}}}}$. The two norm of an ${\displaystyle m\times m}$ matrix ${\displaystyle A}$ is defined by ${\displaystyle \max _{{\vec {v}}\neq {\vec {0}}}{\frac {||A{\vec {v}}||_{2}}{||{\vec {v}}||_{2}}}}$ where ${\displaystyle {\vec {v}}}$ is an m-dimensional vector that is not the zero vector.