Banded Householder representation of linear subspaces

Details Banded Householder representation of linear subspaces Banded Householder representation of linear subspaces

2011-08-30

arxiv.org/abs/1108.5822v3

Computer Science

Numerical Analysis

5 pages, 1 figure, submitted to Linear Algebra and its Applications

Scientific paper

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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