Computational Techniques

Imperial College - Department of Computing - 2021-2022

Manon Flageat & Luca Grillotti

Based on the materials of Abbas Edalat

Lecture Notes

Part 1 - Linear Algebra reviews

Author: Manon Flageat & Luca Grillotti

Link

Parts 1&2 - Lecture Notes

Authors: Luca Grillotti & Manon Flageat

Link

Slides - Part 1

January 18th

Content:

  • [Review] Vector and Matrix

  • [Review] Vector Spaces

Module Introduction

Slides - Before

Slides - After

January 20th

Content:

  • [Review] Scalar Product

  • [New] Vector and Matrix Norms

Slides Before

Slides After

January 25th

Content:

  • [Review] Linear Map in R^n

  • [Review] Eigenvalues and Eigenvectors

Slides Before

Slides After

January 27th

Content:

  • [Review] Diagonalisation

  • [New] Generalised Eigenvectors

Slides Before

Slides After

Slides - Part 2

Introduction

Extension Linear Maps to C

Orthogonal Matrices

Spectral Decomposition

Positive Definite Matrices (1)

Singular Value Decomposition

Cholesky Decomposition

Least Square Methods