Free module · Quantitative toolkit
Linear Algebra
The moment you hold two positions you are doing linear algebra, whether you know it or not.
portfolio
The building blocks
- A vector is an ordered list of numbers.
- Match entries by position before combining them.
- Read vectors and dot products
- Multiply matrices and solve equations
- Model covariance and shared factors
Lessons in this module
- Start with lists: addition, scaling and a dot product
- Your portfolio is a vector; your risk is a matrix
- Eigenvalues: where the risk actually lives
- Regression, conditioning, and regularisation
Practice and apply
- Two-asset portfolio variance by hand — Asset A: σ = 30%, weight 60% · Asset B: σ = 15%, weight 40% · ρ = 0.4
- Reading a scree plot — Correlation matrix of 6 strategies has eigenvalues 3.9, 1.2, 0.5, 0.2, 0.15, 0.05
- Dot product — Find (2,3) · (4,5).
Work through the practice exercises · Quant development tools