# Linear Algebra — Content Fill Progress

## Status: ✅ Complete (2026-05-20)

## Sections

- [x] **Linear systems of equations** (23411) — 36 nodes filled
- [x] **Matrices** (23447) — 147 nodes filled (incl. 17 Echelon children + 23 siblings)
- [x] **Linear systems and matrices** (23751) — 25 nodes filled
- [x] **Vector spaces** (23775) — 57 nodes filled
- [x] **Applications** (24113) — 8 nodes filled (2 inaccessible: 403)

## Summary

**Total: ~273 nodes filled** across 5 sections.

## Empty nodes (not in scope)

- **24121, 24122** — 403 Forbidden (deleted/owned by another user)
- **External nodes** (116, 316, 424, etc.) — Parent/root nodes from other topics

## Content Coverage

- **Basic terminology** — All foundational definitions
- **Gaussian elimination** — REF/RREF, Gauss-Jordan, extended RREF with four subspaces
- **Matrix theory** — Operations, types, decompositions (LU, QR, SVD), canonical forms
- **Invertible Matrix Theorem** — 30+ equivalent conditions
- **Vector spaces** — Coordinate and abstract, subspaces, bases, dimension, isomorphism
- **Linear transformations** — Kernel, range, isomorphisms, eigenvalues, Cayley-Hamilton
- **Applications** — Differential equations, Markov chains, coding theory, Leontief model