{R}R Dev Notes

Found total of 8 articles.

8.4 PCA and Spectral Methods

An intuitive, in-depth explanation of PCA, spectral clustering, and eigenvector-based data analysis. Covers covariance matrices, graph Laplacians, and why eigenvalues reveal hidden structure in data. Concludes Chapter 8 and leads naturally into SVD in Chapter 9.

2025-10-10

8.3 The QR Algorithm (High-Level Intuition)

A clear, intuitive, and comprehensive explanation of the QR algorithm—how repeated QR factorizations reveal eigenvalues, why orthogonal transformations provide stability, and how shifts and Hessenberg reductions make the method efficient. Ends with a smooth bridge to PCA and spectral methods.

2025-10-09

8.2 Rayleigh Quotient

An intuitive and comprehensive explanation of the Rayleigh quotient, why it estimates eigenvalues so accurately, how it connects to the power method and inverse iteration, and why it forms the foundation of modern eigenvalue algorithms. Ends with a natural transition to the QR algorithm.

2025-10-08

8.1 Power Method and Inverse Iteration

A clear, practical, and intuitive explanation of the power method and inverse iteration for computing eigenvalues. Covers dominance, repeated multiplication, shifted inverse iteration, and real applications in ML, PCA, and large-scale systems. Smoothly introduces the Rayleigh quotient.

2025-10-07

Chapter 8 — Eigenvalues and Eigenvectors

A deep, intuitive introduction to eigenvalues and eigenvectors for engineers and practitioners. Explains why spectral methods matter, where they appear in real systems, and how modern numerical algorithms compute eigenvalues efficiently. Leads naturally into the power method and inverse iteration.

2025-10-06

7.4 Why QR Is Often Preferred

An in-depth, accessible explanation of why QR decomposition is the preferred method for solving least squares problems and ensuring numerical stability. Covers orthogonality, rank deficiency, Householder reflections, and the broader role of QR in scientific computing, with a smooth transition into eigenvalues and eigenvectors.

2025-10-05

1.4 A Brief Tour of Real-World Failures

A clear, accessible tour of real-world numerical failures in AI, ML, optimization, and simulation—showing how mathematically correct algorithms break inside real computers, and preparing the reader for Chapter 2 on floating-point reality.

2025-09-06

Numerical Linear Algebra: Understanding Matrices and Vectors Through Computation

Learn how linear algebra actually works inside real computers. A practical guide to LU, QR, SVD, stability, conditioning, and the numerical foundations behind modern AI and machine learning.

2025-09-01

Search Logs

Hello World bot 1238 IT assistant bot 1210 Deploy Teams bot to Azure 1207 Microsoft Bot Framework 1105 Teams bot development 1085 Teams production bot 1075 bot for sprint updates 1061 Zendesk Teams integration 1048 Teams app zip 1044 Microsoft Teams Task Modules 1026 Teams chatbot 1024 Bot Framework Adaptive Card 1020 Teams bot tutorial 1013 Bot Framework example 1008 Task Modules 1007 Teams bot packaging 1005 Bot Framework proactive messaging 995 C 993 Graph API token 991 Bot Framework CLI 978 Azure CLI webapp deploy 976 Bot Framework prompts 971 Adaptive Card Action.Submit 965 Azure App Service bot 952 Microsoft Graph 935 Azure Bot Services 933 Adaptive Cards 906 ServiceNow bot 906 Azure bot registration 904 identity in Teams 870

Development & Technical Consulting

Working on a new product or exploring a technical idea? We help teams with system design, architecture reviews, requirements definition, proof-of-concept development, and full implementation. Whether you need a quick technical assessment or end-to-end support, feel free to reach out.