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Curriculum / Phase 1 · Common Quantitative Core

Linear Algebra, Optimisation and Numerical Methods

Study matrix methods, optimisation and numerical techniques for quantitative finance models and calibration.

Why study Linear Algebra, Optimisation and Numerical Methods?

Portfolio weights, risk factors and calibration problems all become numerical systems. Learn to judge whether the answer is stable and economically sensible, as well as whether a solver reports success.

Who this is for

For learners who know elementary calculus and want the computational foundations of portfolio and pricing models.

What you should be able to do

  • Solve linear systems and interpret least-squares geometry.
  • Connect eigenvalues and factor methods to covariance models.
  • Use optimisation, root-finding and numerical integration with attention to stability.

An example of the work this prepares you for

A small numerical model with a benchmark solution, a sensitivity check and an explanation of its numerical limitations.

Prerequisites and suggested preparation

You should be comfortable with the background covered in these programmes. Equivalent knowledge from university study or independent learning is also suitable.

A preview of the learning journey

The lessons build towards these kinds of reasoning and practical work.

Read models geometrically

Connect matrices and projections to risk and estimation.

Choose under constraints

Explain the trade-offs behind an optimisation result.

Check numerical reliability

Recognise conditioning, approximation error and fragile calibration.

Members work through the detailed lessons, derivations, worked examples and solutions inside the learning dashboard.

Explore lesson previews by topic

Open a topic preview to see its introduction, learning objectives and prerequisites. Previous and next links let you explore the lessons in study order. Full lessons are available in the member dashboard; selected samples are free to read in full.

Topic previewLinear systems and least squares3 lessonsTopic previewSpectral and factor methods3 lessonsTopic previewOptimisation2 lessonsTopic previewNumerical methods and calibration4 lessonsTopic previewVectors, Linear Combinations, and the Dot Product3 lessonsTopic previewSolving Linear Systems and Matrix Algebra5 lessonsTopic previewVector Spaces, Subspaces, and the Four Fundamental Subspaces6 lessonsTopic previewLinear Transformations, Matrix Representation, and Rank-Nullity5 lessonsTopic previewDeterminants4 lessonsTopic previewEigenvalues, Diagonalisation, and Dynamical Applications5 lessonsTopic previewSymmetric Matrices and the Eigenstructure Toolkit2 lessonsTopic previewIntroduction to the Singular Value Decomposition2 lessonsTopic previewInner Product Spaces and Orthogonality5 lessonsTopic previewQR Factorisation and Least Squares5 lessonsTopic previewAdjoints, Self-Adjoint, and Normal Operators4 lessonsTopic previewThe Spectral Theorem4 lessonsTopic previewPositive Definite Matrices, Quadratic Forms, and Quadrics6 lessonsTopic previewThe Full Singular Value Decomposition4 lessonsTopic previewLow-Rank Approximation, PCA, and Applications5 lessonsTopic previewFloating-Point Arithmetic, Conditioning, and Stability4 lessonsTopic previewEigenvalue Computation Algorithms5 lessonsTopic previewIterative Methods and Sparse Matrices4 lessons

Free resources to start learning

Use these alongside the programme or to prepare independently. Start with the introductory material, work through an example, then return to the research papers when the underlying ideas are familiar.

  1. Textbook · Free

    Introduction to Applied Linear Algebra

    Stephen Boyd and Lieven Vandenberghe

    Work through least squares and applied matrix examples in the free author-hosted book.

  2. University course · Free

    Linear Algebra

    MIT OpenCourseWare · Gilbert Strang

    Use the university problem sets for deeper matrix intuition.

  3. Video lectures · Free

    Applied Linear Algebra on YouTube

    Stanford · ENGR108

    Watch the companion lectures when a geometric explanation helps.

  4. Textbook · Free

    Convex Optimization

    Stephen Boyd and Lieven Vandenberghe

    Progress to constrained problems and optimality conditions after linear algebra.

Links reviewed 14 October 2026. Free refers to the linked reading, notes or videos; printed books and certificates may cost extra.

Find more papers and learning materials in the SelfMadeQuant Directory.

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