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Thread: A few matrix checks

  1. #1
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    A few matrix checks

    I have 3 eigenvectors for a matrix M, I have normalised them so that U^t*M*U is a diagonal matrix (U^t is the transpose of U).
    How do i know which eigenvector goes in which column of U.

    Also I have been asked to find the diagonal matrix formed by U^t*M*U.
    Is there any way to make this easier to find, as this will require multiplying a lot of fractions with surds everywhere...
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    Quote Originally Posted by deragon999 View Post
    I have 3 eigenvectors for a matrix M, I have normalised them so that U^t*M*U is a diagonal matrix (U^t is the transpose of U).
    How do i know which eigenvector goes in which column of U.

    Also I have been asked to find the diagonal matrix formed by U^t*M*U.
    Is there any way to make this easier to find, as this will require multiplying a lot of fractions with surds everywhere...
    $\displaystyle U^TMU$ will be a diagonal matrix, and the entries along the diagonal will be the eigenvalues of $\displaystyle M$, in whatever order you placed the corresponding eigenvectors in $\displaystyle U$.
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  3. #3
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    Thanks, i never knew that.

    Does it not matter the order you put the normalised vectors as columns of U then?
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    Quote Originally Posted by deragon999 View Post
    Thanks, i never knew that.

    Does it not matter the order you put the normalised vectors as columns of U then?
    No, but the order you put them in will determine the order of the entries of the diagonal matrix, as I explained.
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