Computational Techniques - 2021-2022

Computational Techniques

Imperial College - Department of Computing - 2021-2022

Manon Flageat & Luca Grillotti

Based on the materials of Abbas Edalat

Part 1 - Linear Algebra reviews

Parts 1&2 - Lecture Notes

Slides - Part 1

Slides - Part 2

Extension Linear Maps to C

Orthogonal Matrices

Spectral Decomposition

Positive Definite Matrices (1)

Singular Value Decomposition

Cholesky Decomposition

QR Decomposition

Least Square Methods

Revision Session

Lecture Notes

Part 1 - Linear Algebra reviews

Author: Manon Flageat & Luca Grillotti

Parts 1&2 - Lecture Notes

Authors: Luca Grillotti & Manon Flageat

Slides - Part 1

January 18th

Content:

[Review] Vector and Matrix
[Review] Vector Spaces

Module Introduction

Slides - Before

January 20th

Content:

[Review] Scalar Product

[New] Vector and Matrix Norms

January 25th

Content:

[Review] Linear Map in R^n
[Review] Eigenvalues and Eigenvectors

January 27th

Content:

[Review] Diagonalisation
[New] Generalised Eigenvectors

Slides - Part 2

Introduction

Extension Linear Maps to C

Orthogonal Matrices

Spectral Decomposition

Positive Definite Matrices (1)

Singular Value Decomposition

Cholesky Decomposition

QR Decomposition

Least Square Methods

Revision Session

Link to Exercises with Solutions

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