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Why any matrix of $SU(2)$ is unitary diagonalizable?

I know from here why any matrix of $SU(2)$ is diagonalizable? that any matrix of $SU(2)$ is diagonalizable but why it is unitary diagonalizable?

Could anyone explain this for me please?

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A matrix is unitary diagonalizable if and only if it is normal: Normal Matrix, Wolfram MathWorld. Every matrix in $SU(2)$ is normal, and the result follows.

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  • $\begingroup$ and if we want to show that any matrix in $SU(2)$ is special unitary diagonalizable what shall we do ? $\endgroup$
    – Secretly
    Apr 6, 2019 at 10:09

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