Similarity reduction of a general matrix to Hessenberg form

With several algorithms for finding the eigensystem of a matrix the volume of work is greatly reduced if the matrix A is first transformed to upper-Hessenberg form, i.e. to a matrix H such that h, ij 0 (i> i+1). The reduction may be achieved in a stable manner by the use of either stabilized elementary matrices or elementary unitary matrices [2].