One of the defining properties of a [[Vector]]. To get the magnitude of a vector, you can treat the vector's Cartesian coordinates as the $x$ and $y$ of a triangle. $\huge||\vec{v}|| = \sqrt{ \vec{v}_{0}^{2} + \vec{v}_{1}^{2} + \cdots }$ Magnitudes are **never** negative The more generalized notion of magnitude or 'length' is that for some [[Vector Space]] $V$ the magnitude of an element $A\in V$ is equal to the square root of the [[Inner Product]] of $A$ with itself. $\huge \lvert \lvert A \rvert \rvert = \sqrt{ \braket{A,A} } $