How could I prove that a unitary and upper triangular matrix A MUST be a diagonal matrix?
$\displaystyle U$ unitary $\displaystyle \Longrightarrow U^{*}=U^{-1}\Longrightarrow $ also $\displaystyle U^{*}$ , in a rather trivial way, is unitary, but it is LOWER triangular , and since the inverse of an upper triangular (invertible ) matrix is upper triangular then...
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