Orthosymmetric block rotations

Abstract

Abstract. Rotations are essential transformations in many parts of numerical linear algebra. In this paper, it is shown that there exists a family of matrices unitary with respect to an orthosymmetric scalar product J, that can be decomposed into the product of two J-unitary matrices-a block diagonal matrix and an orthosymmetric block rotation. This decomposition can be used for computing various one-sided and two-sided matrix transformations by divide-and-conquer or treelike algorithms. As an illustration, a blocked version of the QR-like factorization of a given matrix is considered.