The claim is that the RSI operation is just finding a fixed point of improvement,
replyRSI(LLM) = RSI(LLM) -- for an optimal LLM* which is a fixed point of RSI
As for eigenvalues/vectors, they're fixed points of (1/val)A or A*val
Eigenvectors represent fixed directions, not fixed magnitudes. From Wikipedia:
reply> More precisely, an eigenvector v of a linear transformation T is scaled by a constant factor lambda when the linear transformation is applied to it: Tv = lambda v .
In other words, repeated multiplication of an eigenvector by a matrix can still create exponential growth.