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Math Help - Finding eigenvectors and eigenvalues geometrically

  1. #1
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    Finding eigenvectors and eigenvalues geometrically

    Find the eigenvalues and eigenvectors of A geometrically.


    A=
    [1 0
    0 1]


    (projection onto the x-axis)
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  2. #2
    Newbie vincent's Avatar
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    the matrix for the projection on the x axis is
    <br />
\left( \begin{array}{ccc} 1 & 0 \\<br />
0 & 0<br />
\end{array} \right)<br /> <br />

    and since eigenvectors
    are the vectors
    x which satisfy Ax={\lambda}x with A the matrix of your linear transformation and {\lambda} an eigenvalue of A, the eigenvectors of the projection on the x axis must be all the vectors that are already on the x axis and have an eigenvalue of 1. you can also see this by observing the matrix which is already diagonnal and gives you right away its only eigenvalue 1.





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  3. #3
    MHF Contributor Bruno J.'s Avatar
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    There is also the eigenvalue 0, which corresponds to...
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  4. #4
    Newbie vincent's Avatar
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    aaaaaaaaaaaaaah yess yes yes 0, of course! merci de me doublechecker bruno
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  5. #5
    MHF Contributor Bruno J.'s Avatar
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    Haha! Avec plaisir.

    The eigenspace corresponding the the eigenvalue 0, in this case, is the vertical line through the origin; vectors on this line are projected to the zero vector.
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