Название: Linear Algebra for Data Science
Автор: Moshe Haviv
Издательство: World Scientific Publishing
Год: 2023
Страниц: 257
Язык: английский
Формат: pdf (true)
Размер: 10.5 MB

This book serves as an introduction to linear algebra for undergraduate students in Data Science, statistics, Computer Science, economics, and engineering. The book presents all the essentials in rigorous (proof-based) manner, describes the intuition behind the results, while discussing some applications to Data Science along the way.The book comes with two parts, one on vectors, the other on matrices. The former consists of four vector algebra, linear independence and linear subspaces, orthonormal bases and the Gram-Schmidt process, linear functions. The latter comes with eight matrices and matrix operations, invertible matrices and matrix inversion, projections and regression, determinants, eigensystems and diagonalizability, symmetric matrices, singular value decomposition, and stochastic matrices. The book ends with the solution of exercises which appear throughout its twelve chapters.

Linear algebra is linear algebra is linear algebra. So why does the title refer to Data Science? The answer is that the content of this text is what I believe is what students in Data Sciences need to know. I tried not to put here what I believe they can do without. Moreover, when exposing students to the notation for vectors and matrices, I am avoiding using physical interpretations such as forces. Best for Data Sciences students to have in mind an array with figures when they visualize a vector. Likewise, for a matrix.

With the exception of Chapter 12, besides high school algebra, there are minimal prerequisites for this text. The text refers a few times to the statistical concepts of (empirical) mean, variance and covariance. There is no need for prior exposure to linear regression. With a few exceptionsa, there is no assumption for any previous knowledge in calculus. Some ease with polynomials is required for Chapter 9. Chapter 12 deals with stochastic matrices. Some knowledge in elementary probability is required there and admittedly without completing a basic course in probability, the content of this chapter may appear as not having sufficient motivation. It is also the only chapter where some results are left unproved.