Why does x-axis have eigenvalue = 1

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Homework Help Overview

The discussion revolves around the concept of eigenvalues, specifically why the x-axis is associated with an eigenvalue of 1 and the y-axis with an eigenvalue of -1. Participants are trying to understand the context in which these eigenvalues are presented, particularly in relation to a function or transformation described by their lecturer.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the specific function associated with the eigenvalues and the meaning behind the lecturer's diagram. There is a request for clarification on how eigenvalues relate to vectors and functions in this context.

Discussion Status

Some participants are exploring potential functions that could explain the eigenvalues mentioned, while others express uncertainty about the subject matter being discussed. There is no explicit consensus on the interpretation of the lecturer's explanation, but there is engagement in considering possible functions that relate to the eigenvalues.

Contextual Notes

There is mention of a diagram drawn by the lecturer, which may lack sufficient context for participants to fully grasp the underlying concepts. The discussion reflects a need for more information regarding the specific function or transformation being referenced.

Natasha1
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Why has the x-axis have an eigenvalue = 1 and the y-axis an eigenvalue =-1? (please stay simple in your answers)
 
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Could you be more specific? An eigenvalue as I understand it is generally associated with a function and a vector. I don't understand what the function is here.
 
LeonhardEuler said:
Could you be more specific? An eigenvalue as I understand it is generally associated with a function and a vector. I don't understand what the function is here.

Our lecturer, just drew a diagram the other day on the board with an arrow pointing to the x-axis with lambda = 1 and another arrow with lambda = -1 pointing to the y-axis? Does anyone get what he was trying to explain? Many thanks
 
Maybe he was talking about the eigenvalues of some particular function which had the unit vectors in the x- and y-directions as eigenvectors. For example, the function f([x,y])=[x,-y] has the unit vectors [1,0] and [0,1] as eigenvectors with these eigenvalues because f([1,0])=[1,0]=1*[1,0] and f([0,1])=[0,-1]=-1*[0,1]. Or maybe he was talking about something entirely different. It's hard to say since I don't know what subject he was discussing.
 
LeonhardEuler said:
Maybe he was talking about the eigenvalues of some particular function which had the unit vectors in the x- and y-directions as eigenvectors. For example, the function f([x,y])=[x,-y] has the unit vectors [1,0] and [0,1] as eigenvectors with these eigenvalues because f([1,0])=[1,0]=1*[1,0] and f([0,1])=[0,-1]=-1*[0,1]. Or maybe he was talking about something entirely different. It's hard to say since I don't know what subject he was discussing.

I think that was it. Thanks :-)
 

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