Understanding Linear Mapping: A Non-Technical Explanation

In summary, a linear mapping is a function or relation that connects elements from one set to elements of another set, and in order to be considered a linear mapping, it must follow the rule that f(ax+by) = af(x) + bf(y).
  • #1
Cardebaun
1
0
Hello,

so i was looking up the defintion of linear mapping and mapping in general and i have seen the technical defintion a few times but i was wondering if someone would mind explaining it to me in more general english. How would you explain it instead of just pointing out the definition?

What i have gotten so far is that it is an operation performed to transfer(not sure if I'm using this word in the correct mathematical sense) an equation to another vector space.

please correct me if I'm wrong thanks.
 
Physics news on Phys.org
  • #2
A "mapping" from one set to another is any function or relation that associates every member of the "domain" set to a member of the "range" set.

To have a linear mapping, you need vector spaces rather than general sets so that you can define "ax+ by" for numbers a and b and vectors x and y. Then a mapping is "linear" if and only if f(ax+ by)= af(x)+ bf(y).
 

1. What is linear mapping?

Linear mapping, also known as linear transformation, is a mathematical concept used to describe the relationship between two vector spaces. It involves the transformation of one vector space into another in a linear and consistent manner.

2. How is linear mapping different from other types of mappings?

Linear mapping is different from other types of mappings because it follows the rules of linearity. This means that the mapping preserves the properties of addition and scalar multiplication. In simpler terms, the outputs of a linear mapping are always a multiple of the inputs.

3. What are the applications of linear mapping?

Linear mapping has many applications in fields such as physics, engineering, economics, and computer science. It is used to model real-world systems, make predictions, and solve problems that involve multiple variables.

4. How is linear mapping represented?

Linear mapping can be represented in various ways, such as through matrices, graphs, and equations. Matrices are commonly used to represent linear mappings because they make it easier to perform calculations and visualize the transformation.

5. Can you give an example of linear mapping?

One example of linear mapping is a simple scale transformation, where the input vector is multiplied by a constant factor to produce the output vector. For instance, if the input vector is (2, 4) and the scaling factor is 3, the output vector will be (6, 12).

Similar threads

I A = norm-preserving linear map (+other conditions) => A = lin isometry
    • Linear and Abstract Algebra
Replies
4
Views
853
I Terminologies used to describe tensor product of vector spaces
    • Linear and Abstract Algebra
Replies
7
Views
197
I Explanation of a Line of a proof in Axler Linear Algebra Done Right 3r
    • Linear and Abstract Algebra
Replies
4
Views
1K
MHB Mapping linear spaces to nonlinear ones.
    • Linear and Abstract Algebra
Replies
1
Views
1K
I Number of Binary Operations on a Set with a Special Property
    • Linear and Abstract Algebra
Replies
2
Views
433
MHB Find Linear Mapping: Help Solving $V \setminus (W_1 \cup \cdots \cup W_m)$
    • Linear and Abstract Algebra
Replies
22
Views
3K
MHB Show the Linear Map is Diagonalizable
    • Linear and Abstract Algebra
Replies
1
Views
1K
I Difference between 'Field' (algebra) and 'Field' (geometry)
    • Linear and Abstract Algebra
Replies
12
Views
3K
MHB Solving Linear Mapping Problems with Matrix $M$ in $\mathbb K^2$
    • Linear and Abstract Algebra
Replies
10
Views
3K
I Linear Bezier curve projection
    • Linear and Abstract Algebra
Replies
1
Views
1K

Hot Threads

Recent Insights

Back
Top