What Is a Linear Relationship?

There is a linear function relationship between two variables, which is said to have a linear relationship between them. Proportional relationship is a special case of linear relationship, inverse proportional relationship is not a linear relationship. More generally, if these two variables are used as the horizontal and vertical coordinates of a point, respectively, and the image is a straight line on a plane, then the relationship between the two variables is a linear relationship. That is, if a binary linear equation can be used to express the relationship between two variables, the relationship between these two variables is called a linear relationship. Therefore, a binary linear equation is also called a linear equation. By extension, a linear equation with n variables is also called an n-ary linear equation, but this has nothing to do with a straight line.

The salient feature of the linear relationship is that the image is a straight line that passes through the origin (in the absence of a constant term, such as: y = kx + jz, (k, j is a constant, x, z is a variable); and when the image is a straight line that does not When the function is called

Given a vector group A : 1, 2, ... n, and a vector b , if a set of numbers k 1, k 2, ..., kn exists, such that

Linear relationship of vectors

Then the vector b can be said to be linearly represented by the vector group A. It is also said that the vector b is a linear combination of the vector group A , and k 1, k 2, ..., kn are called the coefficients of this linear combination ^[1] .

The vector b can be represented linearly by the vector group A, that is, the system of linear equations

Linear relationship of vectors

There are solutions.

There are vector groups A : 1, 2, ... n, and B : 1, 2, ..., n. If each vector in vector group B can be linearly represented by vector group A , it is called a vector Group B can be represented linearly by vector group A ; if vector group A and vector group B can be expressed linearly with each other, then these two vector groups are called equivalent and denoted by A B ^[1] .