Index: Linear Algebra

Linear algebra is not about matrices. It’s about structure — how to capture relationships, compress information, and reveal hidden symmetries in the world.

Why Linear Algebra Matters

Every time Google ranks web pages, every time your phone recognizes your face, every time an AI generates text — linear algebra is there, working in the background. It’s the mathematical language of systems that are too complex to understand piece by piece, but simple enough to understand as a whole.

This is not a textbook. It’s a journey through the key ideas that make linear algebra powerful: from the humble system of equations to the spectral theorem, from concrete calculations to geometric intuition. Each article builds on the last, but each also stands alone.

(These notes helped me score 100% in MAT223.)

Articles

Part I: Foundations

1. Re-imagining Matrices
2. Solving Linear Systems
3. Vectors in Euclidian Space
4. Matrix Operations

Part II: Transformations

5. Matrix Transformations as Functions
6. Subspaces
7. Kernel and Image
8. Orthogonality and Projections

Part III: Structure

9. The Determinant
10. Eigenvalues and Eigenvectors
11. Diagonalization and Similarity
12. Orthogonal Diagonalization and the Spectral Theorem
13. Singular Value Decomposition

Part IV: Applications in Quantitative Finance

14. Portfolio Optimization
15. PCA in Finance
16. Covariance Estimation and Regularization