Magnitude
In mathematics, magnitude refers to the size, length, or quantity of a mathematical object, regardless of its direction. For vectors, it represents the absolute length of the vector, while for real numbers, it is the absolute distance from zero.
Example
For a two-dimensional vector $\mathbf{v} = (x, y)$, its magnitude is denoted as $|\mathbf{v}|$ and is calculated using the Pythagorean theorem: $$|\mathbf{v}| = \sqrt{x^2 + y^2}$$ If $\mathbf{v} = (3, -4)$, then its magnitude is $|\mathbf{v}| = \sqrt{3^2 + (-4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.