Linear Algebra and Its Applications with R

ISBN-13: 9780367486846 / Angielski / Twarda / 2021 / 406 str.

Ruriko Yoshida

Opis

The book developed from the need to teach a linear algebra course to students focused on data science and bioinformatics programs. 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.

Spis treści

Preface. 1. Systems of Linear Equations and Matrices. 1.1. Introductory Example from Statistics. 1.2. What is a Matrix? What is a Vector? 1.3. Systems of Linear Equations. 1.4. Echelon Form. 2. Matrix Arithmetic. 2.1. Introductory Example from Statistics. 2.2. Matrix Operations. 2.3. Properties of Matrix Operations and Matrix Inverse. 2.4. Elementary Matrices. 2.5. Discussion. 3. Determinants. 3.1. Introductory Example from Astronomy. 3.2. Determinants. 3.3. Introduction of Determinants. 3.4. Properties of Determinants. 3.5. Cramer's Rule. 3.6. Discussion. 4. Vector Spaces. 4.1. Introductory Example from Data Science. 4.2. Vector Spaces and Subspaces. 4.3. Null Space, Column Space, and Row Space. 4.4. Spanning Sets and Bases. 4.5. Coordinates Systems and Change of Basis. 4.6. Discussion. 5. Inner Product Space. 5.1. Introductory Example from Statistics. 5.2. Inner Products. 5.3. Angles and Orthogonality. 5.4. Discussion. 6. Eigen Values and Eigen Vectors. 6.1. Introductory Example from Data Science: Image Compression. 6.2. Eigen Values and Eigen Vectors. 6.3. Diagonalization. 6.4. Discussion. 7. Linear Regression. 7.1. Introductory Example from Statistics. 7.2. Simple Linear Regression. 7.2. Simple Linear Regression. 8. Linear Programming. 8.1. Introductory Example from Optimization. 8.2. Linear Programming. 9. Network Analysis. 9.1. Introductory Example from Network Analysis. 9.1. Introductory Example from Network Analysis. 9.2. Graphs and Networks. 9.3. Discussion. Appendices. A) Introduction to RStudio via Amazon Web Service (AWS). B) B Introduction to R. Bibliography. Index.

O autorze

Dr. Ruriko Yoshida is an Associate Professor of Operations Research at the Naval Postgraduate School. She received her Ph.D. 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.