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I Building a Unitary Matrix from a Non-Unitary Matrix

  1. May 19, 2017 #1
    Suppose I have some arbitrary square matrix [itex]M[/itex], and I want to build a unitary matrix [itex]U[/itex]: [tex]U=\left[\begin{array}{c|c}M & N \\\hline O & P\end{array}\right][/tex] Does there exist some general procedure for determining [itex]N[/itex], [itex]O[/itex], and [itex]P[/itex] given [itex]M[/itex]?
     
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  3. May 20, 2017 #2

    Orodruin

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    No, it may not be possible to do this depending on M.
     
  4. May 20, 2017 #3

    Orodruin

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    Also, it depends on the size of your new matrix relative to ##M##. Apart from the fact that you must ensure that ##\sum_i |M_{ij}|^2## and ##\sum_j |M_{ij}|^2##. That being said, when you do have the possibility of constructing a matrix like that, I would first rewrite ##M## as ##M_0 V##, where ##V## is a unitary matrix and ##M_0## is hermitian. Then you might get some inspiration from https://arxiv.org/abs/1107.3992
     
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