  In further pursuit of the diagonalizable \emph{real nonnegative inverse
eigenvalue problem} (RNIEP), we study the relationship between the \emph{row
cone} $\mathcal{C}_r(S)$ and the \emph{spectracone} $\mathcal{C}(S)$ of a
Perron similarity $S$. In the process, a new kind of matrix, \emph{row Hadamard
conic} (RHC), is defined and related to the D-RNIEP. Characterizations are
given when $\mathcal{C}_r(S) = \mathcal{C}(S)$, and explicit examples are given
for all possible set-theoretic relationships between the two cones. The
symmetric NIEP is the special case of the D-RNIEP in which the Perron
similarity $S$ is also orthogonal.

Spectral Theory