Why does x-axis have eigenvalue = 1

[Natasha1]

Why has the x-axis have an eigenvalue = 1 and the y-axis an eigenvalue =-1? (please stay simple in your answers)

 

[LeonhardEuler]

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.

 

[Natasha1]

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

 

[LeonhardEuler]

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.

 

[Natasha1]

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 :-)