# TODO: Linear Algebra Content Progress

# Linear Algebra — Content Fill Progress

## Status: In Progress✅ Complete (2026-05-20)

## Sections

- [ x] **Linear systems of equations** (23411) — ~30 child36 nodes⏎
- [  filled
- [x] **Matrices** (23447) — ~100 child130 nodes⏎
- [  filled
- [x] **Linear systems and matrices** (23751) — ~20 child25 nodes⏎
- [  filled
- [x] **Vector spaces** (23775) — ~60 child57 nodes⏎
- [  filled
- [x] **Applications** (24113) — ~10 child nodes⏎
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## Node-level tracking
⏎
See individual section 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 detailed progress.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

# Parents

* Linear algebra