Its true that one can say a unitary matrix takes the form(adsbygoogle = window.adsbygoogle || []).push({});

[itex]U=e^{iH}[/itex]

where [itex]H[/itex] is a Hermitian operator. Thats great, and it makes sense, but how can you compute the matrix form of [itex]H[/itex] if you know the form of the unitary matrix [itex]U[/itex]. For example, suppose you wanted to find [itex]H[/itex] given that the unitary matrix is one of the familiar rotation matrices (2 x 2) for simplicity. Let's say

[itex]U=\left(\begin{array}{cc} cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta) \end{array}\right)[/itex]

What would the procedure be in finding the matrix form of [itex]H[/itex]? I suppose you could start by finding the eigensystem of the unitary matrix. Then, upon normalizing the eigenbasis of [itex]U[/itex], somehow you could find the matrix representation of [itex]H[/itex]. Any pointers or suggestions would be great.

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# A Unitary Matrix and Hermitian Matrix

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