QR Factorization in Matrix Algebra with R and Rcpp

Matrix decomposition is a cornerstone of modern data science, scientific computing, and statistical modeling. Understanding how to break down complex matrices into simpler, computationally efficient components is essential for solving linear systems and least-squares problems. This course provides a clear, step-by-step guide to QR factorization, showing you how to decompose matrices into orthogonal and upper triangular parts using R and high-performance C++ libraries. You will learn the fundamental theory of matrix algebra before moving on to practical, high-performance implementations. Through structured written explanations, you will explore how to write efficient code that bridges R with low-level libraries like Armadillo and Eigen using Rcpp. What you will learn: Understand the mathematical foundations of QR factorization and orthogonal matrices; Implement QR decomposition algorithms from scratch using standard R code; Leverage Rcpp to integrate high-performance C++ code directly into your R workflows; Utilize the Armadillo library for efficient linear algebra operations and matrix manipulations; Apply the Eigen library to optimize numerical computations and speed up matrix decompositions; Compare the performance of different implementation strategies to write optimized code. The course begins with core definitions and the mathematical theory of matrix decomposition, then transitions into hands-on implementation using R, Rcpp, and advanced C++ linear algebra libraries. This course is designed for beginners in numerical computing, data analysts, and R programmers looking to enhance their computational math skills. No advanced C++ experience is required, though a basic familiarity with R programming is recommended. Start mastering high-performance matrix algebra today.