Phase 5
Numerical Linear Algebra & Computing
Phase 5 of the Quant Academy curriculum.
5.1Full Lesson
Floating-Point Arithmetic, Conditioning, and Stability
Why finite-precision numbers are enough - and the two independent things that can still ruin an answer.
5.2Full Lesson
LU Factorization and Solving Linear Systems
Gaussian elimination as a matrix factorization, why we pivot, and the two triangular solves that do the real work.
5.3Full Lesson
QR Factorization and Least Squares
Orthonormal bases from Gram-Schmidt, why the modified version keeps its orthogonality, and the stable route to regressio
5.4Full Lesson
Cholesky Factorization and Positive-Definite Systems
The symmetric, twice-as-fast factorization - and the engine that turns independent normals into a correlated portfolio.
5.5Full Lesson
Eigenvalue & SVD Algorithms and Iterative Methods
Why we iterate instead of solving a characteristic polynomial, from power iteration to the QR algorithm and conjugate gr