Block reflector

Block reflector

"A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one."
* see abstract here http://locus.siam.org/SINUM/volume-25/art_0725014.html

It is built out of many elementary reflectors.

It is also referred to as a triangular factor, and is a triangular matrix and they are used in the Householder transformation

LAPACK routines

Here are some of the LAPACK routines that apply to block reflectors
* "*larft" forms the triangular vector T of a block reflector H=I-VTVH.
* "*larzb" applies a block reflector or its transpose/conjugate transpose as returned by "*tzrzf" to a general matrix.
* "*larzt" forms the triangular vector T of a block reflector H=I-VTVH as returned by "*tzrzf".
* "*larfb" applies a block reflector or its transpose/conjugate transpose to a general rectangular matrix.

ee also

* Reflection (mathematics)
* Householder transformation
* Unitary matrix
* Triangular matrix


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