1. norm is a function 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 defining 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.
2. If a norm is defined in a linear space, it is called a normed linear space.
1 and norm 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 defining 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.
2. Matrix norm is a common basic concept in the fields of matrix theory, linear algebra and functional analysis in mathematics. When a matrix space is established as a normed vector space, it is the norm of matrix equipment. In application, the mapping between finite-dimensional normed vector spaces is often expressed in the form of matrix, and the norm of equipment in the mapping space can also be expressed in the form of matrix norm.
However, there is no recognized and unique method to measure the norm of matrix.
Extended data:
Norm is a basic concept in mathematics. In functional analysis, it is defined in a normed linear space and satisfies certain conditions, that is, ① non-negative; ② Homogeneity; ③ Triangle inequality. It is usually used to measure the length or size of each vector in a vector space (or matrix).
References:
Norm _ Baidu Encyclopedia?