Find the eigenvalues of cos(x) -sin(x)

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    Eigenvalues
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Homework Help Overview

The discussion revolves around finding the eigenvalues of two matrices involving trigonometric functions, specifically cosine and sine. The matrices presented are 2x2 and involve expressions that suggest a connection to rotational transformations.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss calculating the characteristic polynomial and express uncertainty about finding roots of the resulting quadratic equation.

Discussion Status

Some guidance has been offered regarding the use of the quadratic formula to find roots, but there is no explicit consensus on the next steps or the interpretation of the results.

Contextual Notes

There is mention of an unknown variable L in the quadratic equation, indicating that the discussion may be constrained by the need to solve for this variable in the context of the eigenvalue problem.

stukbv
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How do i find the eigenvalues of

cos(x) -sin(x)
sin(x) cos(x)

and

cos(x) sin(x)
sin(x) -cos(x)

Thanks
 
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Hi stukbv! :smile:

I would start by calculating the characteristic polynomial...
 


Hi, i have done that but i get L^2 - 2Lcos(x) + 1 = 0. How do i find a root??
 

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