Skip to content
LeadAfrik
Intermediate · Self-paced2026 Edition

Linear Algebra for Quant Finance

The linear algebra a working quant actually uses — vectors and matrices as the language of portfolios, covariance, factor models, and regression. Twelve modules from vector geometry to SVD and PCA, with every theorem grounded in a finance use case: portfolio risk, factor extraction, yield-curve decomposition, Cholesky simulation, and the numerical traps that bite production code.

12

Modules

~11h 15m

Reading time

Intermediate

Level

Self-paced

Format

§

Syllabus

  1. 01

    Why linear algebra is the language of finance

    Portfolios are vectors. Covariance is a matrix. Factor models are decompositions. Everything quant collapses to linear algebra.

    ~35 minModule 01
    →
  2. 02

    Vectors, spaces, norms, inner products

    Vectors as geometric objects and as data. Norms (L1, L2, L∞) and what each measures. Inner products and angles.

    ~55 minModule 02
    →
  3. 03

    Matrices and the four operations

    Matrix multiplication as composition of linear maps. Transpose, trace, determinant — what each tells you about a matrix.

    ~55 minModule 03
    →
  4. 04

    Linear systems and Gaussian elimination

    Solving Ax = b. Existence, uniqueness, and the four cases. LU decomposition and why it scales.

    ~55 minModule 04
    →
  5. 05

    Rank, the four fundamental subspaces, and projections

    Column space, null space, row space, left null space. Rank-nullity. Projections onto subspaces — the geometric heart of OLS.

    ~60 minModule 05
    →
  6. 06

    Least squares and QR decomposition

    OLS as a projection. The normal equations. QR via Gram-Schmidt and why it beats the normal equations numerically.

    ~60 minModule 06
    →
  7. 07

    Eigenvalues, eigenvectors, diagonalization

    What eigen-pairs mean geometrically. Diagonalization and what it buys you. The characteristic polynomial.

    ~60 minModule 07
    →
  8. 08

    Symmetric matrices, the spectral theorem, PSD

    Why covariance matrices are special. Positive semi-definite, Cholesky factorization, the eigen-spectrum of a covariance.

    ~60 minModule 08
    →
  9. 09

    SVD — the master decomposition

    Singular value decomposition: every matrix factorises as UΣVᵀ. Geometric picture, low-rank approximation, the workhorse behind PCA.

    ~65 minModule 09
    →
  10. 10

    PCA, factor extraction, and yield-curve geometry

    PCA derived from the SVD. Variance explained. Level/slope/curvature factors in the Kenyan yield curve.

    ~60 minModule 10
    →
  11. 11

    Matrix calculus for optimisation

    Gradient and Hessian of quadratic forms. Derivative of xᵀAx. The exact identities that drive every portfolio optimisation.

    ~55 minModule 11
    →
  12. 12

    Numerical linear algebra in practice

    Conditioning, stability, Cholesky for portfolio simulation, when to use NumPy vs LAPACK directly, the traps that wreck production code.

    ~55 minModule 12
    →

How to use this course

Start with module 01 if the material is new; skip ahead if you have prior exposure. Each module is self-contained but the arc is sequential — the projects in the final module assume the toolkit from modules 1-11. Every module ends with key takeaways and a curated further-reading list with primary sources.