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 formula_1 belonging to formula_2 can be written in the form :
formula_3 where formula_4 is the identity matrix for formula_2, formula_6 is a scalar and formula_7 belongs to formula_8 .
LAPACK routines.
Here are some of the LAPACK routines that apply to block reflectors