"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 belonging to can be written in the form : where is the identity matrix for , is a scalar and belongs to .
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.
See also Reflection (mathematics) Householder transformation Unitary matrix Triangular matrix
References