Foundations

Numerical Linear Algebra

Learn linear algebra through programming, numerical experiments, and quantum-computing applications.

Overview

Understand the project, then explore the work.

Resources open inside this site. Guides, papers, figures, notebooks, and source files are organized around the project’s story.

About this project

This repository is aimed at providing an introduction to the basics of linear algebra and advanced computational numerical linear algebra with a focus on applications in quantum computing.

Quantum computing is a rapidly growing field that has the potential to revolutionize the way we process and analyze information. Linear algebra forms an essential part of the mathematical framework used in quantum computing. In this article, we will explore the role of linear algebra in quantum computing, including its importance in representing quantum states, quantum gates, and quantum algorithms.

Check the full Blog series here

Table

- Introductory Linear Algebra

Collections

Module

Course guide

1 curated item

PaperHow computers represent data

Module

Core linear algebra

11 curated items

NotebookScalars, Vectors, Matrices And Tensors NotebookThe Trace Operator NotebookThe Determinant NotebookMultiplying Matrices And Vectors NotebookIdentity And Inverse Matrices NotebookLinear Dependence And Span

Supporting material in Core linear algebra5 items

NotebookNorms NotebookSpecial Kind Of Matrices And Vectors NotebookEigendecomposition NotebookSingular Value Decomposition NotebookThe Moore Penrose Pseudoinverse

Module

Advanced methods

8 curated items

Section notes

This course is focused on the question: How do we do matrix computations with acceptable speed and accurancy?

The course is taught in python with jupyter notebooks, using libraries like Scikit-learn and Numpy as well as Numba ( a library that compiles Python to C for faster performance) and PyTorch ( an alternative to Numpy for the GPU)

1. Why are we here?

We start with a high level overview of some foundational concepts in numerical linear algebra. Matrix and tensor products Matrix Decompositions Accuracy Memory Use Speed Parallelization & vectorization

NotebookWeek 1 Introduction To Matrices NotebookWeek 2 Singular Value Decomposition NotebookWeek 3 Topic Modeling With NMF And SVD NotebookWeek 4 Background Removal With Robust PCA NotebookWeek 5 Compressed Sensing CT Scans Robust Regression NotebookWeek 6 Health Outcomes With Linear Regression

Supporting material in Advanced methods2 items

NotebookWeek 7 How To Implement Linear Regression NotebookWeek 8 Page Rank With Eigen Decomposition

Module

GIFs

1 result figure

Numerical Linear Algebra

Understand the project, then explore the work.

Table

Course guide

Core linear algebra

Advanced methods

Table of Contents

1. Why are we here?

GIFs