# Matrix-Based Introduction to Multivariate Data Analysis

Textbook

1. Front Matter
Pages i-xix
2. ### Elementary Statistics with Matrices

1. Front Matter
Pages 1-1
Pages 3-16
Pages 17-29
Pages 31-45
3. ### Least Squares Procedures

1. Front Matter
Pages 47-47
Pages 49-64
Pages 65-80
Pages 81-94
Pages 95-107
4. ### Maximum Likelihood Procedures

1. Front Matter
Pages 109-109
Pages 111-130
Pages 131-148
Pages 149-163
Pages 165-177
Pages 179-194
5. ### Miscellaneous Procedures

1. Front Matter
Pages 195-195
Pages 197-209
Pages 211-228
Pages 229-245
Pages 247-258

1. Front Matter
Pages 259-259
Pages 261-277
Pages 279-295
Pages 297-310
Pages 311-339
Pages 341-359
Pages 361-382
7. Back Matter
Pages 383-457

### Introduction

This is the first textbook that allows readers who may be unfamiliar with matrices to understand a variety of multivariate analysis procedures in matrix forms. By explaining which models underlie particular procedures and what objective function is optimized to fit the model to the data, it enables readers to rapidly comprehend multivariate data analysis. Arranged so that readers can intuitively grasp the purposes for which multivariate analysis procedures are used, the book also offers clear explanations of those purposes, with numerical examples preceding the mathematical descriptions.

Supporting the modern matrix formulations by highlighting singular value decomposition among theorems in matrix algebra, this book is useful for undergraduate students who have already learned introductory statistics, as well as for graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis.

The book begins by explaining fundamental matrix operations and the matrix expressions of elementary statistics. Then, it offers an introduction to popular multivariate procedures, with each chapter featuring increasing advanced levels of matrix algebra.

Further the book includes in six chapters on advanced procedures, covering advanced matrix operations and recently proposed multivariate procedures, such as sparse estimation, together with a clear explication of the differences between principal components and factor analyses solutions. In a nutshell, this book allows readers to gain an understanding of the latest developments in multivariate data science.

### Keywords

Statistics Multivariate Analysis Data Analysis Matrices Vectors Sparse Estimation