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Math Help - Orthogonal Matrices

  1. #1
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    Orthogonal Matrices

    A and B are orthogonal.

    Orthogonal Matrices-h.png

    Where H is the Householder transformation. According to the book, the result should be -b, not b. I reasoned since a and b were orthogonal that a^t b =0. It is true that H_a a =-a. Any ideas?
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  2. #2
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    Re: Orthogonal Matrices

    Hey Hal2001.

    If a and b are orthogonal then I agree that the whole right term should disappear since matrix multiplication is associative so you can calculate (2/c*a)*(a^t*b) = blah * 0 = 0.

    But why are you assuming a is orthogonal to b? Is that assumed in your work or by your teacher?
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  3. #3
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    Re: Orthogonal Matrices

    Hello,

    The book gives a is orthogonal to b.
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  4. #4
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    Re: Orthogonal Matrices

    Well what you did looks right: I can't really fault what you've done if a^t*b = 0 and all the operations are associative which they are if they are matrices.
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  5. #5
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    Re: Orthogonal Matrices

    Okay thanks. Probably just a typo.
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