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Math Help - Orthogonal Matrix

  1. #1
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    Orthogonal Matrix

    Prove that the transpose of an orthogonal matrix is an orthogonal matrix.

    I think that the kroenecker delta needs to be used but not sure how to write it out.
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  2. #2
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    Quote Originally Posted by dwsmith View Post
    Prove that the transpose of an orthogonal matrix is an orthogonal matrix.

    I think that the kroenecker delta needs to be used but not sure how to write it out.

    What's the definition of "orthogonal matrix" you have? One of the equivalent ones is that a (real) square matrix A is orthogonal iff A^{-1}=A^t\Longleftrightarrow AA^t=I .

    From here that your problem has an almost trivial proof.

    Tonio
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    (AA^{T})^{T}=(A^{T})^{T}A^{T}=AA^{T}=I

    Therefore, the transpose of an orthogonal matrix is orthogonal.
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    Quote Originally Posted by dwsmith View Post
    (AA^{T})^{T}=(A^{T})^{T}A^{T}=AA^{T}=I

    Therefore, the transpose of an orthogonal matrix is orthogonal.

    Indeed

    Tonio
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