Matrix Theory - Isometries
Find the eigenvalues and eigenvectors of A.
See attached file for full problem description.
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 March 4, 2021, 5:36 pm ad1c9bdddfhttps://brainmass.com/math/linear-algebra/matrix-theory-isometries-2405
Solution Preview
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:
(cost-x)(-cost-x)-sint*sint=0 so:
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 ...
Solution Summary
This shows how to find eigenvalues and eigenvectors.
$2.49