unitary and upper triangular matrix => diagonal matrix

**dannyboycurtis** · December 10th 2009, 04:12 PM

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

**tonio** · December 10th 2009, 06:52 PM

Originally Posted by dannyboycurtis

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

$U$ unitary $\Longrightarrow U^{*}=U^{-1}\Longrightarrow$ also $U^{*}$ , 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

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