Lineal Transformation basis change

In summary, the conversation discusses the canonical bases of ℝ^3 and ℝ^2, with C^3 being the canonical base of ℝ^3 and C^2 being the canonical base of ℝ^2. The person in the conversation mentions trying a transformation using vectors from the canonical basis and checks for correctness. They also mention moving the conversation to a more appropriate section for Linear Algebra doubts.
  • #1
SqueeSpleen
141
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Find


http://imageshack.us/a/img35/1637/lineal2.gif


http://imageshack.us/a/img210/1370/lineal1.gif




C^3 is the canonical base of ℝ^3, C^2 is the canonical base of ℝ^2

I tried:
http://imageshack.us/a/img822/6274/lineal3.gif


But I'm not sure if this is right, I made a mistake here or I'm not checking this right.
I think, if this is well done I have to have the same answer when putting the vectors of canonical basis (1,0,0), (0,1,0), (0,0,1), the result in canonical ℝ^2 has to be the same result that I got if I use (1,0,1), (1,1,1), (1,0,0) in ℝ^2 using B'

I hope I was clear enough, I don't speak English very well.
 
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  • #2
This isn't pre-calculus. You should move this into the "calculus and beyond," section.
 
  • #3
camjohn said:
This isn't pre-calculus. You should move this into the "calculus and beyond," section.

Please report such things instead of replying in the thread.
 
  • #4
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1. What is a lineal transformation basis change?

A lineal transformation basis change is a mathematical process in which the basis (a set of linearly independent vectors) of a vector space is changed to a new basis. This involves expressing the original vectors in terms of the new basis vectors, and finding a transformation matrix that can convert coordinates from the original basis to the new basis.

2. Why is a lineal transformation basis change important?

A lineal transformation basis change is important because it allows us to understand and analyze vector spaces in different ways. By changing the basis, we can simplify calculations and gain new insights into the properties of the vector space.

3. How is a lineal transformation basis change related to linear algebra?

A lineal transformation basis change is a fundamental concept in linear algebra. It is closely related to the concept of a linear transformation, which is a function that preserves vector addition and scalar multiplication. The transformation matrix used in a basis change is a key tool in solving linear algebra problems.

4. What are some real-world applications of lineal transformation basis change?

Lineal transformation basis change has many applications in fields such as engineering, computer graphics, and physics. It is used to simplify calculations and solve problems involving vector spaces, such as determining the motion of objects in 3D space or analyzing the behavior of electrical circuits.

5. Are there any limitations to lineal transformation basis change?

While lineal transformation basis change is a powerful tool, it does have some limitations. It can only be applied to vector spaces that have a finite number of dimensions. Additionally, the transformation matrix used in a basis change must be invertible, meaning it has a unique inverse matrix.

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