The set in which all elements in algebraic space are mapped to zero elements is called kernel, and it is recorded as ker；. The set of all the mapping elements on set A is called the mapping image set, and is denoted as ImA.

Suppose there is a linear mapping f: w->; V, w space is mapped to v space.

Im f？ It is equivalent to the range of F, that is, for any W, it belongs to W, and f(w) is within the sphere of influence in V; Mathematical language Imf=f(W).

Kerr F is equivalent to the null space of F, that is, the original image corresponding to point 0 in V. This original image is not unique, but a set, that is, Kerr F; The mathematical language Ker f={w belongs to w where w makes f(w)=0}.

Extended data

Definition of linear transformation

1, linear transformation is the mapping of linear space v to itself, which is usually called transformation on v.

2. Linear transformation is an object of linear algebra research, that is, the mapping from vector space to its own operation. For example, for an arbitrary linear space v, the potential is a linear transformation on v, and the translation is not a linear transformation on v.

3. In abstract algebra, a linear mapping is a homomorphism of a vector space, or a morphism in a category formed by a vector space in a given domain.

4. In mathematics, linear mapping (also called linear transformation or linear operator) is a function between two vector spaces, which keeps the operations of vector addition and scalar multiplication. The term "linear transformation" is particularly commonly used, especially for linear mapping (endomorphism) from vector space to itself.

References:

Baidu Encyclopedia-Linear Transformation