Matrix Theory - Isometries
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Find the eigenvalues and eigenvectors of A.
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Consider the matrices in O(2) of the form:
these matrices correspond to the elements of O(2) with det(A)= -1. Find the eigenvalues and eigenvectors of A.© BrainMass Inc. brainmass.com May 24, 2023, 12:48 pm ad1c9bdddf
I will use t instead of theta, it is easier to write; to find the eigenvalues we need to solve Det(A-xI)=0, which means:
x^2=1 (using that the cos^2+sin^2=1).
So x1=1 and x2=-1 are the eigenvalues.
In what follows we will assume sint non-zero. If sint is zero, we discuss in the end of the proof what the answer is.
Eigenvectors for ...
This shows how to find eigenvalues and eigenvectors.