Block reflector

"A block reflector is an orthogonal, symmetric matrix that reverses a subspace whose dimension may be greater than one."

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 : $$ Q = I -auu^T $$ where $$I$$ is the identity matrix for $$\mathcal M_n(\R) $$, $$a$$ is a scalar and $$u$$ belongs to $$\R^n$$.

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.