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Math Help - Orthogonal Matrices and the dot product

  1. #1
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    Orthogonal Matrices and the dot product

    If A is an n x n real matrix, how would I start each part of a proof that A is an orthogonal matrix iff Ax dot Ay = x dot y for all x and y in Rn?
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  2. #2
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    Re: Orthogonal Matrices and the dot product

    start with the fact that x \cdot y = x^Ty, where the right-hand side is a matrix product of a 1xn and an nx1 matrix.
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  3. #3
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    Re: Orthogonal Matrices and the dot product

    Thanks so much! I think I got. I used the fact that A^-1 = A^t iff A is an orthogonal matrix!

    Thank you again!
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