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For the most part, LAPACK represents unitary matrices like $\mathbf U$ as products of householder reflectors, and provides specialized routines to work with that representation (for instance, use [dormqr] to multiply by $\mathbf U$, or [dorgqr] to explicitly tabulate $\mathbf U$ into a dense matrix). If you already have $\mathbf U$ in householder format, it ...

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