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1. (mathematics) A measure of length given by "the square root of the squares." Denoted by ||·||_2, the two-norm of a vector \vec v= is ||\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 \max_{\vec v≠\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.