Lexic.us

Definition of Two-norm

1. Noun. Mathematical measure of length given by "the square root of the squares." Denoted by $||\backslash cdot||\_2$, the two-norm of a vector is $||\backslash vec\; v||\_2=\backslash sqrt\{a\_1^2+a\_2^2+\backslash cdots+a\_n^2\}$. The two norm of an $m\backslash times\; m$ matrix $A$ is defined by $\backslash max\_\{\backslash vec\; v\backslash neq\backslash vec\; 0\}\backslash frac\{||A\backslash vec\; v||\_2\}\{||\backslash vec\; v||\_2\}$ where $\backslash vec\; v$ is an m-dimensional vector that is not the zero vector. ¹

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