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  1. #1
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    orthogonal matrix

    Show that matrix A is orthogonal...

    I know that to be orthogonal the dot product must equal to 0.
    but how do i go on about showing that this matrix is orthogonal??

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    Hello,

    A matrix is orthogonal if MM^t = M^t M = Id

    If M=(a_{ij}), M^t = (a_{ji})
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    Quote Originally Posted by b00yeah05 View Post
    Show that matrix A is orthogonal...

    I know that to be orthogonal the dot product must equal to 0.
    but how do i go on about showing that this matrix is orthogonal??

    Consider the rows of the matrix (or the columns - it doesn't matter) as vectors.

    If each of these 3 vectors have the length 1 and form an orthonormal basis then the matrix is orthogonal.
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    from my definition it says that it is orthonormal if...

    ||vi|| = 1 or vi.vi = 1

    so to work out the length i get the sqrt of the squred values..but what do you mean by orthonormal basis in your comment there? im guessing that it is important as its in bold..
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  5. #5
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    Quote Originally Posted by b00yeah05 View Post
    from my definition it says that it is orthonormal if...

    ||vi|| = 1 or vi.vi = 1

    so to work out the length i get the sqrt of the squred values..but what do you mean by orthonormal basis in your comment there? im guessing that it is important as its in bold..
    The v's must be mutually perpendicular .... v1 . v2 = 0, v1 . v3 = 0, v2 . v3 = 0
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