Talk:Elementary reflector
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rm from article: The routines in LAPACK "*LARZ" apply an "elementary reflector" H to a M-by-N matrix, from either the left or the right. The elementary reflector is expressed as
- H = I − τ v· v′
where τ is a scalar and v is a vector. H is a product of k elementary reflectors.
A block reflector is formed out of k elementary reflectors by the routines "*LARZT", which forms the triangular factor T of a block reflector H of order > n.
[edit] LAPACK routines
- "*larf" applies an elementary reflector to a general rectangular matrix.
- "*larfc" applies the conjugate transpose of an "elementary reflector" to a general matrix.
- "*larfg" generates an elementary reflector Householder matrix.
- "*larzc" applies (multiplies by) the conjugate transpose of an elementary reflector as returned by "*tzrzf" to a general matrix.
- "*larz" applies an elementary reflector as returned by "*tzrzf" to a general matrix.
- "*tzrzf" reduces the upper trapezoidal matrix A to upper triangular matrix.
