The Generalized Householder Transformation and Sparse Matrices

Many algorithms for solving eigenvalue, least squares and nonlinear programming problems require the determination of an orthogonal matrix Q such that for a given matrix, C, Q trandforms C into an upper triangular matrix, QC. Usually Q is a product of Householder transformations. Each transformation is a rank 1 correction of the identity matrix designed to annihilate elements in one vector.