Linear Algebra and Its Applications with R

Ruriko Yoshida

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367486846
• eBook ISBN: 9781000400267
• Edition: 1
• Topic: Economics
• Subtopic: Algebra
• Index: Economics

This book developed from the need to teach a linear algebra course to students focused on data science and bioinformatics programs. These students tend not to realize the importance of linear algebra in applied sciences, since traditional linear algebra courses tend to cover mathematical contexts but not the computational aspect of linear algebra or its applications to data science and bioinformatics.

The author presents the topics in a traditional course, yet offers lectures as well as lab exercises on simulated and empirical data sets. This textbook provides students a theoretical basis which can then be applied to the practical R and Python problems, providing the tools needed for real-world applications.

Each section starts with working examples to demonstrate how tools from linear algebra can help solve problems in applied sciences. These exercises start from easy computations, such as computing determinants of matrices, to practical applications on simulated and empirical data sets with R so that students learn how to get started with R, along with computational examples in each section, and then students learn how to apply what they've learned to problems in applied sciences.

This book is designed from first principles to demonstrate the importance of linear algebra through working computational examples with R and Python, including tutorials on how to install R in the Appendix. If a student has never seen R, they can get started without any additional help.

Since Python is one of the most popular languages in data science, optimization, and computer science, code supplements are available for students who feel more comfortable with Python. R is used primarily for computational examples to develop students' practical computational skills.

About the Author:

Dr. Ruriko Yoshida is an Associate Professor of Operations Research at the Naval Postgraduate School. She received her PhD in Mathematics from the University of California, Davis. Her research topics cover a wide variety of areas: applications of algebraic combinatorics to statistical problems such as statistical learning on non-Euclidean spaces, sensor networks, phylogenetics, and phylogenomics. She teaches courses in statistics, stochastic models, probability, and data science.

1

Systems of Linear Equations and Matrices

DOI: 10.1201/9781003042259-1

Solving a system of linear equations appears in many problems in academic and non-academic disciplines since this is one of the simplest and most effective models to solve practical problems in many areas. The working example is a two-way contingency table from categorical data analysis, a classic form of analysis from statistics. The walking example in this chapter is from statistics. Categorical data analysis is one of classical statistical analysis and the example is called a two-way contingency table from categorical data analysis.

1.1 Introductory Example from Statistics

Table 1.1 is from [16] and it records the month of birth and death for 82 descendants of Queen Victoria. This data is used to analyze an association, i.e., relation, between birth-month and death-month. It used to be thought that there were some relations between people's birth-month and death-month. Tables like Table 1.1 are called two-way contingency tables and particularly we call Table 1.1 a $12\times 12$ cont...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Dedication
• Contents
• Preface
• 1 Systems of Linear Equations and Matrices
• 2 Matrix Arithmetic
• 3 Determinants
• 4 Vector Spaces
• 5 Inner Product Space
• 6 Eigen Values and Eigen Vectors
• 7 Linear Regression
• 8 Linear Programming
• 9 Network Analysis
• Appendices
• Bibliography
• Index