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Math Help - orthogonal matrix

  1. #1
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    orthogonal matrix

    two problems that I have problem with:

    1. let A be orthogonal matrix that is triangular, prove that A is diagonal.

    2.let <br />
R^n  = U_1  + U_2 <br /> <br />
be true, does <br />
R^n  = U_1 ^ \bot   + U_2 ^ \bot  <br /> <br />
and if it is why???

    Thanks ahead
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  2. #2
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    Quote Originally Posted by omert View Post
    two problems that I have problem with:

    1. let A be orthogonal matrix that is triangular, prove that A is diagonal.
    Say A is upper triangular.

    This means AA^T = I.
    The inverse of a upper triangular matrix is upper triangular.
    But A^T is lower triangular.
    Thus, A^T is both upper and lower triangular.
    Thus, A^T is diagnol which means A is diagnol.
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