  This paper, on subdominant eigenvalue location of a bordered diagonal matrix,
is the mathematical sequel to an accounting paper by Gao, Ohlson, Ostaszewski
\cite{GaoOO}. We explore the following characterization of dividend-policy
irrelevance (DPI) to equity valuation in a multi-dimensional linear dynamics
framework $L$: DPI occurs under $L$ when discounting the expected dividend
stream by a constant interest rate iff that rate is equal to the dominant
eigenvalue of the canonical principal submatrix $A$ of $L.$ This is justifiably
the `latent' (or gross) rate of return, since the principal submatrix relates
the state variables to each other but with dividend retention. We find that DPI
reduces to the placement of the maximum eigenvalue of $L$ between the dominant
and subdominant eigenvalues of $A.$ We identify a special role, and a lower
bound, for the coefficient measuring the year-on-year dividend-on-dividend
sensitivity in achieving robust equity valuation (independence of small
variations in the dividend policy).
