Linear Algebra & Matrix Methods

Eigendecomposition, singular value decomposition, and sparse linear systems as the numerical backbone of calibration and risk engines. Covers LU/Cholesky factorisation, condition numbers, and iterative solvers used in production pricing and portfolio optimisation.

5 modules~120 min total

Prerequisites

Calculus and basic analysisFamiliarity with matrix notation (addition, multiplication, determinants)

Modules

01

Vectors, Matrices, and Linear Maps

Easy
Linear AlgebraVector SpacesMatrix MethodsLinear Maps
02

LU and Cholesky Factorisation

Medium
Linear AlgebraMatrix FactorisationNumerical MethodsMonte Carlo
03

Eigendecomposition and the Spectral Theorem

Medium
Linear AlgebraEigendecompositionPCARisk Factor Models
04

Singular Value Decomposition and Condition Numbers

Hard
Linear AlgebraSVDCondition NumbersPseudoinverseNumerical Stability
05

Iterative Solvers for Calibration Problems

Hard
Linear AlgebraIterative SolversConjugate GradientNumerical MethodsCalibration