Nonnegative Matrices That Are Similar to Positive Matrices
Thomas J. Laffey, Raphael Loewy, Helena Šmigoc · SIAM Journal on Matrix Analysis and Applications · 2009
We study the question in which nonnegative matrices are similar to positive matrices first raised by Borobia and Moro in 1997. We identify certain classes of nonnegative matrices that are not similar to positive matrices and solve the problem when an $n\times n$ nonnegative matrix has exactly n or $n+1$ elements equal to zero.