🏔️ You can now predict the destiny of a whole neural circuit from two numbers. Here's the summary.

The system: a(t) = W·a(t−1), a discrete circuit that steps forward in time. Unrolled, that's aᵢ = Wⁱ·a₀.

The prediction, from eigenvalues alone (along an eigenvector, aᵢ = λⁱ·v):
• |λ| > 1 → explode.
• |λ| < 1 → decay to zero.
• |λ| = 1 → sustained.
• complex λ → rotation (spiralling in/out/steady by |λ|).
• The largest eigenvalue dominates the long run.

🤖 The big picture: this is one of the most powerful ideas in applied math — reduce a complicated evolving system to a couple of eigenvalues and instantly know its fate. It underlies RNN stability, exploding/vanishing gradients, and the continuous dynamical systems you'll meet next in NMA. Same tool, everywhere. 🚀