Banded Householder representation of linear subspaces

  title={Banded Householder representation of linear subspaces},
  author={Geoffrey Irving},
Abstract We show how to compactly represent any n -dimensional subspace of R m as a banded product of Householder reflections using n ( m - n ) floating point numbers. This is optimal since these subspaces form a Grassmannian space Gr n ( m ) of dimension n ( m - n ) . The representation is stable and easy to compute: any matrix can be factored into the product of a banded Householder matrix and a square matrix using two to three QR decompositions. 
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  • submitted for publication
  • 2004