Synthetic Data and Generative AI

Chapter 3: Gentle introduction to linear algebra – synthetic time series

Abstract

This simple introduction to matrix theory offers a refreshing perspective on the subject. Using a basic concept that leads to a simple formula for the power of a matrix, I show how it can solve time series, Markov chains, linear regression, linear recurrence equations, pseudoinverse and square root of a matrix, data compression, principal components analysis (PCA) or dimension reduction, and other machine learning problems. These problems are usually solved with more advanced matrix algebra, including eigenvalues, diagonalization, generalized inverse matrices, and other types of matrix normalization. My approach is more intuitive and thus appealing to professionals ...