= Defective repeated eigenvalue in a cyclic conversion model
{title2=$(a+b+c)^2=4(ab+bc+ca)$}
When the displayed equality holds, the two nonzero <eigenvalues> of the <three-state cyclic conversion model> coincide at $\lambda=-(a+b+c)/2$. The positive cyclic rates force each <eigenspace> to have <dimension> at most one: if its $A$ coordinate vanished, the first eigenvector equation would force $C=0$, and then the third would force $B=0$. Thus the repeated <eigenvalue> has only one <eigenvector> direction and the <matrix> is not <diagonalizable>. A length-two <Jordan chain> produces both $e^{\lambda t}$ and $te^{\lambda t}$ transients. The rates $(a,b,c)=(1,4,1)$ give an explicit example with $\lambda=-3$.
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