# Banded Householder representation of linear subspaces

@article{Irving2011BandedHR, title={Banded Householder representation of linear subspaces}, author={Geoffrey Irving}, journal={ArXiv}, year={2011}, volume={abs/1108.5822} }

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.

#### 2 Citations

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- 2011

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Compression and direct manipulation of complex blendshape models

- Computer Science
- ACM Trans. Graph.
- 2011

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#### References

SHOWING 1-5 OF 5 REFERENCES

A Fast ULV Decomposition Solver for Hierarchically Semiseparable Representations

- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 2006

We consider an algebraic representation that is useful for matrices with off-diagonal blocks of low numerical rank. A fast and stable solver for linear systems of equations in which the coefficient… Expand

A Storage-Efficient $WY$ Representation for Products of Householder Transformations

- Mathematics
- 1989

A product $Q = P_{1} \cdots P_{r}$ of m-by-m Householder matrices can be written in the form $Q = I + WY^{T}$ where W and Y are each m-by-r. This is called the WY representation of Q. It is of… Expand

Introduction to Smooth Manifolds

- Mathematics
- 2002

Preface.- 1 Smooth Manifolds.- 2 Smooth Maps.- 3 Tangent Vectors.- 4 Submersions, Immersions, and Embeddings.- 5 Submanifolds.- 6 Sard's Theorem.- 7 Lie Groups.- 8 Vector Fields.- 9 Integral Curves… Expand

Fast and stable algorithms for hierarchically semi-separable representations

- submitted for publication
- 2004