Banded Householder representation of linear subspaces

We show how to compactly represent any n-dimensional subspace of R as a banded product of Householder reflections using n(m − n) floating point numbers. This is optimal since these subspaces form a Grassmannian space Grn(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.