Articles

A detailed, story-driven explanation of the deep connection between the Covariance Matrix, Singular Value Decomposition (SVD), and Principal Component Analysis (PCA), complete with analogies, examples, and Python code.

A detailed, step-by-step guide explaining the covariance matrix, its calculation, and its crucial role in data science, from first principles.

An intuitive, story-driven explanation of QR decomposition, covering why it's used, how it's done via Gram-Schmidt, and its relevance in solving real-world problems like least squares.

An intuitive, story-driven explanation of Singular Value Decomposition (SVD), breaking down why it's used, how it works, and its real-world relevance in fields like image compression and data science.

An intuitive, first-principles explanation of eigen decomposition, covering what it is, why it's done, how to calculate it, and its real-world applications in fields like machine learning and physics.

An intuitive and comprehensive guide to understanding change of basis, from fundamental concepts to the power of eigen decomposition, explained with storytelling and practical examples.

An intuitive, storytelling guide to eigenvectors, eigenvalues, and eigenspaces, explaining how they reveal the hidden structure of linear transformations through visualization and step-by-step examples.

A comprehensive guide to understanding and mastering permutations, from basic factorials to advanced concepts like circular and repeated permutations, complete with formulas and examples.

An in-depth exploration of the scientific method, the criteria for a field to be considered a science, and the crucial differences between genuine science and pseudoscience.

Explore the intuitive meaning of a matrix determinant, understanding its role as a scaling factor and orientation indicator in linear transformations, and its implications for solving systems of linear equations.