One last case. Sometimes a weight matrix has complex eigenvalues (remember: no direction stays on its own line). In a dynamical system, complex eigenvalues produce rotation — the activity spirals.

The size (absolute value) of the complex eigenvalue still sets the fate, but now with a spin:
• |λ| = 1 → a sustained rotation (a steady loop — an oscillation).
• |λ| < 1 → a rotation spiralling inward to zero.
• |λ| > 1 → a rotation spiralling outward to infinity.

🧠 So the type of number tells you the type of behavior: real eigenvalues → straight growth or decay; complex eigenvalues → rotation/oscillation. This is exactly how neuroscientists and ML engineers diagnose whether a circuit will settle, blow up, or oscillate — and it generalizes to the continuous dynamical systems used across the rest of NMA.