Explore BrainMass

Explore BrainMass

    Matrix Theory - Isometries

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 May 24, 2023, 12:48 pm ad1c9bdddf
    https://brainmass.com/math/linear-algebra/matrix-theory-isometries-2405

    Attachments

    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

    ADVERTISEMENT