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
EasyLinear AlgebraVector SpacesMatrix MethodsLinear Maps
02
LU and Cholesky Factorisation
PremiumMediumLinear AlgebraMatrix FactorisationNumerical MethodsMonte Carlo
03
Eigendecomposition and the Spectral Theorem
PremiumMediumLinear AlgebraEigendecompositionPCARisk Factor Models
04
Singular Value Decomposition and Condition Numbers
PremiumHardLinear AlgebraSVDCondition NumbersPseudoinverseNumerical Stability
05
Iterative Solvers for Calibration Problems
PremiumHardLinear AlgebraIterative SolversConjugate GradientNumerical MethodsCalibration