Block reflector Information & Block reflector Links at HealthHaven.com

"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.

A reflector $Q$ belonging to $\mathcal M_n(\R)$ can be written in the form : $Q = I - a u u T$ where $I$ is the identity matrix for $\mathcal M_n(\R)$ , $a$ is a scalar and $u$ belongs to $\mathcal \R^n$ .

[edit] 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.

[edit] See also

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