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Norm
A norm is a mapping that assigns a number to a mathematical object that is intended to describe, in some way, the size of the object.
Explanation
It can represent either the length of a vector, the largest singular value of a matrix, the variation of a sequence, or the maximum of a function.
A norm is symbolized by two vertical lines || · || on the left and right of the object. However, often only one line is used.
Example 1
The absolute value (also called the modulus)
||x|| = |x|
is a norm on the one-dimensional vector spaces formed by the real or complex numbers.
Example 2
The quaternion q = a + bi + cj + dk has a norm (or length) of