Finding eigen values of a 2x2 matrix

[andrey21]

Find the eigenvalues of the following 2x2 matrix:

(0 1)/(-1 0)

Homework Equations

By using the formula (a-λ)(d-λ) -bc I was able to obtain the following:


λ^(2) + 1 = 0
λ^(2) = -1

λ = ± √ (-1)

Is thos correct? Also what relevance does this have on the fixed points?

 

[Mark44]

Find the eigenvalues of the following 2x2 matrix:

(0 1)/(-1 0)

Homework Equations

By using the formula (a-λ)(d-λ) -bc I was able to obtain the following:


λ^(2) + 1 = 0
λ^(2) = -1

λ = ± √ (-1)

Is thos correct? Also what relevance does this have on the fixed points?

Yes, they are correct. You can also write them as λ = ±i.

Regarding fixed points, you might be talking about this: For some vectors x₁ and x₂, Ax₁ = ix₁, and Ax₂ =- ix₂, where A is your matrix. i and -i are the eigenvalues and the x vectors are eigenvectors.

 

[andrey21]

Thanks for that just needed some confirmation:)

I was just reading that if a system has eigen values of i and -i then this corresponds to a 90 degree planar rotation?

I ask because the question I am answering goes on to say.

Use eigen value analysis to dscribe the behaviour of the system.

Any help would be great