Invertibility of irreducible matrices Original Research Article

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, Solovʹev, and Zhang and Gu.