TwovariableThere is a power betweenFunctional relation, it is said that there is a linear relationship between them.Positive proportional relationshipIt is a special case of linear relationship,Inverse proportional relationIt is not a linear relationship.More generally, if these two variables are taken as the abscissa and ordinate of the point respectively, and the image is a straight line on the plane, then the relationship between these 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, the binary linear equation is also called a linear equation.By extension, the linear equation with n variables is also called n-variable linear equation, but it has nothing to do with straight lines.
Chinese name
linear relationship
Foreign name
linear relation
Alias
Positive proportional relationship
Basic expression
Y=kx+b (k, b is a constant, k>0, b=0 is a positive proportional relationship)
The prominent feature of the linear relationship is that the image is a straight line passing through the origin (without a constant term, such as: y=kx+jz, (k, j are constants, x, z are variables);When the image is a straight line without the origin, the function is calledLinear relation。
Linear relationship and linear relationship are different and often confused by everyone.
First of all, each item（Constant termExcept) must be once (this is the most important)
For example: x=y+z+c+v+b
So they (x and y, z, c, v, b are variables) are linear relations, which can be said to be: x and y are linear relations, or y and z are linear relations, etc,
If thefrequencyIf it is not once, it is not linear: x=y * z (here we assume that y and z arevariableinstead ofconstant）, then x and y, or x and z are not linear,
The constant has no effect on whether a linear relationship is formed (assuming that the constant is not 0). For example: x=k * y+l * z+a (k, l is a constant, y, z is a variable, and a is a constant), then x and y, z are still linear, because the term: k * y is once, and l * z is also once,Constant termA No impact
For example, x=7 * y+8 * z is linear, and x=- y-2 * z is linear.X=2 * y * z is nonlinear (because the term 2yz is not linear),
from2D imageIn terms of (assuming that there are only two variables, y and x), the linear equation must be linear, not curved, and not inflectional.
Linear representation of vector
Announce
edit
givenvectorgroupA：α1，α2，…αn，Var and vectorb, if there is a group of numbers k ₁, k ₂,..., kn, so that
Linear relation of vector
Is called vectorbThe vector groupALinear representation, also called vectorbIs a vector groupAOne oflinear combination, k ₁, k ₂,..., kn are called the linear combination ofcoefficient[1]．
The vector b can be expressed linearly by the vector group A, that isLinear equations
Linear relation of vector
There is a solution
Set vector groupA：α1，α2，…αn，andB：β1，β2，…，βn，If vector groupBEach vector in can be represented by a vector groupALinear representation is called vector groupBThe vector groupALinear representation;If the vector groupAAnd vector groupBIf they can be expressed linearly with each other, they are called these twoVector group equivalence, recorded asA≌B[1]．
