# TODO: Linear Algebra Content Progress

# Linear Algebra — Content Fill Progress

## Status: ✅ Complete (2026-05-20)

## Sections

- [x] **Linear systems of equations** (23411) — 36 nodes filled
- [x] **Matrices** (23447) — 130 nodes filled
- [x] **Linear systems and matrices** (23751) — 25 nodes filled
- [x] **Vector spaces** (23775) — 57 nodes filled
- [x] **Applications** (24113) — 10 nodes filled

## Summary

**Total: ~258 nodes filled** across 5 sections of the Linear Algebra graph.

Each node contains:
- Definitions with formal statements
- Theorems with proof sketches or intuition
- Worked examples where appropriate
- Geometric interpretations

## Content Coverage

- **Basic terminology** — All foundational definitions (matrices, equations, solutions)
- **Gaussian elimination** — Echelon forms, row operations, consistency
- **Matrix theory** — Operations, types, decompositions (LU, QR, SVD), canonical forms
- **Invertible Matrix Theorem** — 30+ equivalent conditions for nonsingular matrices
- **Vector spaces** — Coordinate and abstract, subspaces, bases, dimension
- **Linear transformations** — Kernel, range, isomorphisms, eigenvalues
- **Eigenvalue theory** — Characteristic/minimal polynomials, Cayley-Hamilton, Jordan form
- **Applications** — Differential equations, Markov chains, coding theory, Leontief model

## 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, outside Linear Algebra scope
⏎
# Parents

* Linear algebra