We obtain new sufficient conditions for invertibility of an irreducible complex matrix. Remarks are also given on eigenvalues (and the associated eigenvectors) that lie on the boundary of various spectrum inclusion regions of an irreducible matrix. Our results extend, strengthen, or clarify the recent work of Brualdi, Brualdi and Mellendorff, Farid, Solov'ev, and Zhang and Gu.
Relation:
Linear Algebra and Its Applications 259(1-3), pp.39-70