# Linear Algebra

Canonical: https://manyspace.aporia.systems/subjects/mathematics/linear-algebra-31
Updated: 2026-10-13

Linear Algebra: about 39 hours. Each topic lists what you need first and what it unlocks.

## Systems & Matrices

- [Gaussian Elimination](https://manyspace.aporia.systems/topics/gaussian-elimination-mth-linalg-155)
- [Matrix Algebra](https://manyspace.aporia.systems/topics/matrix-algebra-mth-linalg-156)
- [Determinants](https://manyspace.aporia.systems/topics/determinants-mth-linalg-157)

## Vector Spaces

- [Vector Spaces & Subspaces](https://manyspace.aporia.systems/topics/vector-spaces-subspaces-mth-linalg-158)
- [Basis & Dimension](https://manyspace.aporia.systems/topics/basis-dimension-mth-linalg-159)
- [Row Space, Column Space & Nullspace](https://manyspace.aporia.systems/topics/row-space-column-space-nullspace-mth-linalg-160)

## Linear Transformations

- [Linear Maps & Matrices](https://manyspace.aporia.systems/topics/linear-maps-matrices-mth-linalg-161)
- [Eigenvalues & Eigenvectors](https://manyspace.aporia.systems/topics/eigenvalues-eigenvectors-mth-linalg-162)
- [Similarity & Jordan Form Intro](https://manyspace.aporia.systems/topics/similarity-jordan-form-intro-mth-linalg-163)

## Inner Products & Applications

- [Inner Product Spaces](https://manyspace.aporia.systems/topics/inner-product-spaces-mth-linalg-164)
- [Orthogonal Projections & Least Squares](https://manyspace.aporia.systems/topics/orthogonal-projections-least-squares-mth-linalg-165)
- [Spectral Theorem](https://manyspace.aporia.systems/topics/spectral-theorem-mth-linalg-166)
- [Linear Algebra Applications](https://manyspace.aporia.systems/topics/linear-algebra-applications-mth-linalg-167)