The Householder Compressor Theorem and its application in subspace tracking

The energy in a symmetric (r+1)×(r+1) matrix can be transformed perfectly into a smaller r×r submatrix by means of a two-sided Householder transformation. The parameters of this Householder transformation are uniquely determined by the minor eigenvector of the larger matrix. This compressor is the key to a new type of square-root Householder subspace tracker which is optimal in terms of both complexity and performance. Computer experiments validate the theoretical findings.