Nonnegative Matrices Which Are Similar To Positive Matrices

In 1997 A. Borobia and J. Moro first studied the problem of which nonnegative matrices are similar to positive matrices. In 2009 T.J. Laffey, R. Loewy and H. Smigoc proved that a nonnegative irreducible matrix of order n with positive trace and only n (n≥4) or n+1 (n≥3) zero entries are similar to a positive matrix. In this thesis we study the problem for those nonnegative irreducible matrices of order n with positive trace and exactly n+2 zero entries, where n is at least 8. We prove that they can be similar to positive matrices in addition to the other six classes of such matrices.