Girish Mahajan (Editor)

Block reflector

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"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 M n ( R ) can be written in the form : Q = I − a u u T where I is the identity matrix for 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.

    • References

    Block reflector Wikipedia
    (Text) CC BY-SA