The two vertical lines are symbols called norms, which are actually mappings from linear normed space to non-negative real numbers. The two vertical lines are norm and norm, and they are functions with the concept of "length". In the fields of linear algebra, functional analysis and related mathematics, norm is a function that gives all vectors in vector space non-zero positive length or size. A semi-norm can give a nonzero vector a zero length.

The vector space that defines the norm is a normed vector space. Similarly, the vector space that defines a seminorm is a seminormed vector space.

Note: Euclidean norm is defined in two-dimensional Euclidean geometric space R. In this vector space, elements are drawn as a directed line segment with an arrow from the origin, and the length of the directed line segment of each vector is the Euclidean norm of the vector.