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  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

Matrices