How could I prove that a unitary and upper triangular matrix A MUST be a diagonal matrix?

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- Dec 10th 2009, 04:12 PMdannyboycurtisunitary and upper triangular matrix => diagonal matrix
How could I prove that a unitary and upper triangular matrix A MUST be a diagonal matrix?

- Dec 10th 2009, 06:52 PMtonio

$\displaystyle U$ 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...

Tonio