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Math Help - Finding a Hermitian Matrix A^H for a 2 x 3 Matrix A

  1. #1
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    Finding a Hermitian Matrix A^H for a 2 x 3 Matrix A

    Hello,

    I'm having a really hard time with Hermitian matrices.

    In preparation for my exam next week, I've been trying to figure out this problem:

    Given a matrix A = \left| \begin{matrix} i & 1 & i \\<br />
      1 & i & i \end{matrix} \right|, compute A^HA and AA^H.

    How do I find A^H given the 2x3 matrix A?

    Please include all steps. Thank you!
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    A^H=(\bar{A})^t=\begin{bmatrix}{-i}&{\;\;1}&{-i}\\{\;\;1}&{-i}&{-i}\end{bmatrix}^t=\begin{bmatrix}{-i}&{\;\;1}&\\{\;\;1}&{-i}\\{-i}&{-i}\end{bmatrix}
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  3. #3
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    Thank you! That really helped.

    I've moved on to another similar problem, and want to make sure I have the correct A^H.

    If given matrix A = \begin{bmatrix}{1}&{2i}&{i}\\{1}&{i}&{1+i}\end{bma  trix} ,

    would A^H =\begin{bmatrix}{1}&{1}&\\{-2i}&{-i}\\{-i}&{1-i}\end{bmatrix} ?
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    Right.
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