QR Decomposition: Step-by-Step Guide to Solve Linear Equations

QR Decomposition Explained Step-by-Step | Solve Linear Systems with NumPy in Python Learn how QR factorization—decomposing A into an orthogonal matrix Q and an upper-triangular R—solves systems of linear equations efficiently and stably. We cover the theory, algorithms (Gram–Schmidt, Householder), and work through a complete example using Python (NumPy). See how RX = Qᵀb is solved via back substitution and why QR is preferred for ill-conditioned problems. By the end you will: • Understand QR decomposition concepts, types, and steps • Apply QR factorization to solve a system in Python • See real-world applications in engineering, data science, and scientific computing This video is part of my Systems of Linear Equations series: Gauss-Jordan, LU (Doolittle/Crout), Cholesky, QR, Gauss–Seidel, and Conjugate Gradient—each with theory and Python code. Explore all code in my GitHub repository. Perfect for students, engineers, and researchers building numerical methods and Python skills. 🔔 Subscribe and hit the bell so you don’t miss new videos in the series. 👍 Like this tutorial if QR helped you solve a system faster and more stably. 💬 Comment with your questions or the methods you’d like covered next. 🔗 GitHub repo: https://github.com/jubranakram/solvin... #QRDecomposition #LinearAlgebra #NumericalMethods #Python #MathEducation