Computational Linear Algebra with R

Academic coursework and project materials for the "Computational Linear Algebra" course completed during my Master's program in Mathematics with Data Science at the Institute of Mathematics and Applications, Bhubaneswar.

Overview

This repository contains implementations and explorations of fundamental linear algebra concepts using the R programming language. The project focuses on computational approaches to matrix operations, decompositions, and numerical linear algebra techniques.

Contents

• project.Rnw - R Noweb source file containing literate programming implementation
• project.pdf - Compiled PDF report with mathematical derivations and computational results
• README.md - This documentation

Topics Covered

The project explores various computational linear algebra concepts including:

• Matrix operations and properties
• Linear systems solving methods
• Matrix decompositions (LU, QR, SVD, Eigenvalue decomposition)
• Numerical stability and computational considerations
• R implementations of fundamental algorithms
• Performance analysis and optimization techniques

Technical Implementation

R Noweb Format

The project uses R Noweb (.Rnw) format, which combines:

• LaTeX documentation for mathematical notation and explanations
• R code chunks for computational implementations
• Integrated output display and visualization

Key Features

• Mathematical rigor with computational verification
• Step-by-step algorithm implementations
• Performance benchmarking and analysis
• Visualization of mathematical concepts
• Reproducible research methodology

Usage

Prerequisites

• R (version 3.6+)
• Required R packages: base linear algebra libraries
• LaTeX distribution (for PDF compilation)
• knitr package for Noweb processing

Compilation

To regenerate the PDF from source:

library(knitr)
knit('project.Rnw')
# Then compile the resulting .tex file with LaTeX

Academic Context

Course: Computational Linear Algebra
Program: MSc Mathematics with Data Science
Institution: Institute of Mathematics and Applications (IMA), Bhubaneswar
Academic Year: 2020-2022

Learning Outcomes

This project demonstrates proficiency in:

• Theoretical understanding of linear algebra concepts
• Computational implementation of mathematical algorithms
• R programming for scientific computing
• Literate programming and reproducible research
• Mathematical typesetting and technical documentation
• Performance analysis of numerical algorithms

File Structure

R-for-basic-linear-Matrix-algebra/
├── README.md           # Project documentation
├── project.Rnw         # R Noweb source (LaTeX + R code)
└── project.pdf         # Compiled academic report

Key Algorithms Implemented

• Gaussian elimination with partial pivoting
• Matrix factorization methods
• Iterative solvers for linear systems
• Eigenvalue computation algorithms
• Singular value decomposition implementations
• Numerical stability analysis

Applications

The computational techniques explored have applications in:

• Data science and machine learning
• Scientific computing and simulation
• Statistical analysis and modeling
• Engineering problem solving
• Mathematical research

License

Academic work - educational use permitted with proper attribution.

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This repository represents academic coursework completed as part of Master's degree requirements in Mathematics with Data Science specialization.