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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."[1]

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

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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

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References

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  1. ^ Schreiber, Rober; Parlett, Beresford (2006). "Block Reflectors: Theory and Computation". SIAM Journal on Numerical Analysis. 25: 189–205. doi:10.1137/0725014.