Transition Matrices: Solving X[T]X & T(v_1)=v_2

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Discussion Overview

The discussion revolves around understanding a specific page related to transition matrices and linear transformations, particularly focusing on the expressions X[T]X and the mappings T(v_1) = v_2 and T(v_2) = av_1 + bv_2. The scope includes conceptual clarification regarding linear transformations and their representations.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant expresses confusion about the computation of X[T]X and the specific mappings given in the problem.
  • Another participant questions whether the goal is to find the linear transformation based on the properties of the mappings.
  • A participant suggests that the mappings might be an example transformation, but expresses uncertainty about this interpretation.
  • Further responses reinforce the idea that the mappings could be illustrative rather than derived from a specific theory.

Areas of Agreement / Disagreement

Participants generally agree that the mappings may be examples, but there is uncertainty about whether they are derived from a theoretical basis or simply illustrative.

Contextual Notes

There is a lack of clarity regarding the derivation of the mappings T(v_1) = v_2 and T(v_2) = av_1 + bv_2, and whether they are based on established transformations or are merely illustrative examples.

Artusartos
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I am a bit confused about the page that I attached...

I don't understand part (ii)...

How can you compute X[T]X? So why is [tex]T(v_1)=v_2[/tex] and [tex]T(v_2)=av_1 + bv_2[/tex]?

Thanks in advance...
 

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Hey Artusartos.

Are you just trying to find the linear transformation given those properties of how v1 and v2 maps to v1' and v2'?
 
chiro said:
Hey Artusartos.

Are you just trying to find the linear transformation given those properties of how v1 and v2 maps to v1' and v2'?


Hi,


I'm not trying to find anything. I was just trying to undestand the page that I attached (Part ii)...I don't understand why they wrote [tex]T(v_1) = v_2[/tex] and [tex]T(v_2) = av_1 + bv_2[/tex]
 
I think (but am not certain) that this is just an example transformation.
 
chiro said:
I think (but am not certain) that this is just an example transformation.

Oh...so are they just making that up to give an example? I thought they were deriving those equations from somewhere, and that's why I was confused...
 
I'm pretty sure it is just an example.
 
chiro said:
I'm pretty sure it is just an example.

Ok thanks :)
 

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