[eig_circulant ] Some updates on text and code

[longye-tian]

Hi @jstac @thomassargent30

This PR updates the eig_circulant lecture following #946. I’d be grateful if you could take a look when you have a chance.

In response to @jstac 's comments, I have incorporated a little more motivation in the overview and added a formal definition of a circulant matrix using the sphinx-proof definition environment.

This PR also makes a set of small text, notation, and code cleanups discussed in the issue, including removing unnecessary Numba use, clarifying the cyclic-shift convention, fixing the determinant formula, updating transpose notation, and correcting a few typos.

I will open a separate issue for adding exercises, since that seems like a natural follow-up and can be handled separately.

Best,
Longye

[jstac]

🤖 Status note for a future session — from a maintainer investigation on 2026-07-08 into why open-PR previews 404. Context only, not instructions.

Netlify preview: https://pr-952--sunny-cactus-210e3e.netlify.app/ currently returns 404.

Why previews are down (repo-wide findings)

1. This branch is stale — 32 commits behind main. A preview build compiles the whole site from this branch. This branch's lectures/house_auction.md still has unpinned !pip install prettytable, which now breaks on a wcwidth incompatibility. main fixed this on 2026-06-28 by pinning prettytable<3.18 (#939). This alone fails any rebuild of this branch until it's updated to main.

2. The arviz failure was a red herring — do NOT pin arviz or rewrite plotting. A 2026-07-07 rebuild also failed in ar1_bayes/ar1_turningpts with an arviz_plots figsize ValueError. That was a transient bug in an intermediate arviz-plots 1.x release, already fixed in arviz 1.2.0. Verified locally on a clean latest-stack venv: the real az.plot_trace(trace) cell (pymc + numpyro InferenceData) runs green. The lectures use only 1.x-compatible arviz APIs (plot_trace, summary, from_numpyro, compare).

Recommended first step for this PR

Update this branch to main (merge or rebase — pulls in #939 plus ~32 other commits), then let CI rebuild. On today's latest libraries the site builds clean, so the preview should return. house_auction is the known blocker; updating also picks up other since-merged fixes — rebuild and address any remaining per-lecture failures. Verify with:

curl -sI https://pr-952--sunny-cactus-210e3e.netlify.app/eig_circulant.html

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This PR touches: eig_circulant.md. Last CI build: failure@2026-07-07. Branch: 32 commits behind main as of 2026-07-08.

[github-actions]

📖 Netlify Preview Ready!

Preview URL: https://pr-952--sunny-cactus-210e3e.netlify.app

Commit: 29d24ba

📚 Changed Lectures

• eig_circulant

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Build Info

• Workflow: Build Project [using jupyter-book]