Add coverage of non-diagonalisable matrices and the Jordan form (and its effect on linear state-space transients)

[mmcky]

Nothing in the lecture repos covers what happens when a matrix is not diagonalisable. That is a real hole rather than a missing nicety: eigen_I.md in lecture-python-intro teaches eigenvalues, eigenvectors and power iteration, and uses the word "diagonalizable" exactly once, in passing, without ever saying when diagonalisability fails or what to do instead. linear_algebra.md here does not treat it at all. So a reader who meets a defective matrix has nowhere to go.

The natural application is linear state-space dynamics. linear_models.md develops the model, its moments and its stability without an eigendecomposition treatment, so the case where $A = P \Lambda P^{-1}$ does not exist is simply absent — even though it changes the form of the transient: repeated eigenvalues with deficient eigenvectors produce polynomial-times-exponential terms rather than pure exponentials.

This was requested in QuantEcon/meta#28, Tom Sargent's brief on eigenvalues and eigenfunctions, under "Linear state-space dynamics — cases where we require Jordan form", which he noted was "dedicated to Lars Hansen who often raises this case". That issue has been closed against the material that did ship; this is one of the residuals it did not cover.

Suggested shape, in rough order of dependency:

• when diagonalisation fails — algebraic versus geometric multiplicity, and what "defective" means
• the Jordan normal form as the general replacement, with the simplest non-trivial block worked explicitly
• the consequence for dynamics: how a Jordan block changes the transient in a linear state-space model, relative to the diagonalisable case already covered

Worth deciding as part of picking this up: whether the multiplicity material belongs here or as a short addition to eigen_I in lecture-python-intro, with the state-space consequence staying in this repo. The brief filed it under state-space dynamics, which is why it is proposed here.

[mmcky]

Settled: split, as the last paragraph above proposed. Decided while reviewing QuantEcon/meta#344.

The multiplicity and defectiveness prerequisite moves to lecture-python-intro as QuantEcon/lecture-python-intro#808. This issue keeps the state-space consequence.

The reasoning is that the intro gap stands on its own. Checking eigen_I.md directly: it runs to 33 KB, uses "diagonalizable" exactly once — as the precondition on power iteration, "a method for finding the greatest absolute eigenvalue of a diagonalizable matrix" — and never defines it. It has no mention of algebraic or geometric multiplicity, defective matrices, or repeated eigenvalues. So the lecture states a precondition for a method it teaches and gives the reader no way to test it. That is a defect in the intro series regardless of whether anyone ever writes the state-space material, and a reader who meets a defective matrix there should not have to reach the intermediate series to find out what happened.

Revised scope for this issue, once #808 lands:

• the Jordan normal form as the general replacement for diagonalisation, with the simplest non-trivial block worked explicitly
• the consequence for linear_models.md: how a Jordan block changes the transient — polynomial-times-exponential terms rather than pure exponentials — relative to the diagonalisable case already covered

The first bullet of the original suggested shape ("when diagonalisation fails — algebraic versus geometric multiplicity, and what 'defective' means") is now #808's, and can be assumed as a prerequisite here rather than restated.