linear algebra for quantitative finanace

by ZhenghuaJun 10, 20265 views♥ 1

Abstract

This is good for people trying to learn how to visualise and use linear algebra

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This note develops linear algebra from first principles as the working language of machine learning and quantitative finance. It covers vector spaces, the four fundamental subspaces, and matrices as linear maps, then builds to eigendecomposition and the SVD — each worked by hand on small matrices so the abstract theorems become concrete numbers. It treats least squares three ways (normal equations, orthogonal projection, and QR), positive definiteness and quadratic forms, condition number and numerical stability, matrix calculus, and the determinant as signed volume. Throughout, every concept is tied to its ML role: covariance and PCA, regression geometry, regularization and conditioning, and the spectral structure behind dimensionality reduction. Worked examples and exercises connect rank, definiteness, and conditioning directly to regression and portfolio problems.
@wzhenghua23 · Jun 10, 2026