On the effective computation of the inertia of a non-hermitian matrix

Summary given a complex lower Hessenberg matrixA with unit codiagonal, a hermitian matrixH is constructed such that, ifH is non-singular InA= InH. IfA is real,H is real symmetric. Classical results of Fujiwara on the root-separation problem and of Schwarz on the eigenvalue-separation problem are included as special cases.The authors' research was conducted at the Universidade Estadual de Campinas and supported by the Fundação de Amparo à Pesquisa do Estado de São Paulo, Brasil, under grant n⁰ 78/0490.