# Matrix Methods

## 4th Edition

### Applied Linear Algebra and Sabermetrics

**Authors:**Richard Bronson Gabriel Costa

**eBook ISBN:**9780128184202

**Paperback ISBN:**9780128184196

**Imprint:**Academic Press

**Published Date:**18th February 2020

**Page Count:**512

## Description

*Matrix Methods: Applied Linear Algebra and Sabermetrics, Fourth Edition,* provides a unique and comprehensive balance between the theory and computation of matrices. Rapid changes in technology have made this valuable overview on the application of matrices relevant not just to mathematicians, but to a broad range of other fields. Matrix methods, the essence of linear algebra, can be used to help physical scientists-- chemists, physicists, engineers, statisticians, and economists-- solve real world problems.

## Key Features

- Provides early coverage of applications like Markov chains, graph theory and Leontief Models
- Contains accessible content that requires only a firm understanding of algebra
- Includes dedicated chapters on Linear Programming and Markov Chains

## Readership

Advanced UG and Grad Students in advanced linear algebra, applied linear algebra, and matrix algebra courses

## Table of Contents

CHAPTER 1 Matrices

1.1 Basic concepts

Problems 1.1

1.2 Operations

Problems 1.2

1.3 Matrix multiplication

Problems 1.3

1.4 Special matrices

Problems 1.4

1.5 Submatrices and partitioning

Problems 1.5

1.6 Vectors

Problems 1.6

1.7 The geometry of vectors

Problems 1.7

CHAPTER 2 Simultaneous linear equations

2.1 Linear systems

Problems 2.1

2.2 Solutions by substitution

Problems 2.2

2.3 Gaussian elimination

Problems 2.3

2.4 Pivoting strategies

Problems 2.4

2.5 Linear independence

Problems 2.5

2.6 Rank

Problems 2.6

2.7 Theory of solutions

Problems 2.7

2.8 Final comments on Chapter 2

CHAPTER 3 The inverse

3.1 Introduction

Problems 3.1

3.2 Calculating inverses

Problems 3.2

3.3 Simultaneous equations

Problems 3.3

3.4 Properties of the inverse

Problems 3.4

3.5 LU decomposition

Problems 3.5

3.6 Final comments on Chapter 3

CHAPTER 4 An introduction to optimization

4.1 Graphing inequalities

Problems 4.1

4.2 Modeling with inequalities

Problems 4.2

4.3 Solving problems using linear programming

Problems 4.3

4.4 An introduction to the simplex method

Problems 4.4

4.5 Final comments on Chapter 4

CHAPTER 5 Determinants

5.1 Introduction

Problems 5.1

5.2 Expansion by cofactors

Problems 5.2

5.3 Properties of determinants

Problems 5.3

5.4 Pivotal condensation

Problems 5.4

5.5 Inversion

Problems 5.5

5.6 Cramer’s rule

Problems 5.6

5.7 Final comments on Chapter 5

CHAPTER 6 Eigenvalues and eigenvectors

6.1 Definitions

Problems 6.1

6.2 Eigenvalues

Problems 6.2

6.3 Eigenvectors

Problems 6.3

6.4 Properties of eigenvalues and eigenvectors

Problems 6.4

6.5 Linearly independent eigenvectors

Problems 6.5

6.6 Power methods

Problems 6.6

CHAPTER 7 Matrix calculus

7.1 Well-defined functions

Problems 7.1

7.2 Cayley-Hamilton theorem

Problems 7.2

7.3 Polynomials of matricesddistinct eigenvalues

Problems 7.3

7.4 Polynomials of matricesdgeneral case

Problems 7.4

7.5 Functions of a matrix

Problems 7.5

7.6 The function eAt

Problems 7.6

7.7 Complex eigenvalues

Problems 7.7

7.8 Properties of eA

Problems 7.8

7.9 Derivatives of a matrix

Problems 7.9

7.10 Final comments on Chapter 7

CHAPTER 8 Linear differential equations

8.1 Fundamental form

Problems 8.1

8.2 Reduction of an nth order equation

Problems 8.2

8.3 Reduction of a system

Problems 8.3

8.4 Solutions of systems with constant coefficients

Problems 8.4

8.5 Solutions of systemsdgeneral case

Problem 8.5

8.6 Final comments on Chapter 8

CHAPTER 9 Probability and Markov chains

9.1 Probability: an informal approach

Problems 9.1

9.2 Some laws of probability

Problems 9.2

9.3 Bernoulli trials and combinatorics

Problems 9.3

9.4 Modeling with Markov chains: an introduction

Problems 9.4

9.5 Final comments on Chapter 9

CHAPTER 10 Real inner products and least square

10.1 Introduction

Problems 10.1

10.2 Orthonormal vectors

Problems 10.2

10.3 Projections and QR decompositions

Problems 10.3

10.4 The QR algorithm

Problems 10.4

10.5 Least squares

Problems 10.5

CHAPTER 11 Sabermetrics e An introduction

11.1 Introductory comments

11.2 Some basic measures

11.3 Sabermetrics in the classroom

11.4 Run expectancy matrices

11.5 How to “do” sabermetrics

11.6 Informal reference list

11.7 Testing

CHAPTER 12 Sabermetrics e A module

12.1 Base stealing runs (BSRs)

12.2 Batting linear weights runs (BLWTS)

12.3 Equivalence coefficient (EC)

12.4 Isolated power (ISO)

12.5 On base average (OBA)

12.6 On base plus slugging (OPS)

12.7 Power factor (PF)

12.8 Power-speed number (PSN)

12.9 Runs created (RC)

12.10 Slugging times on base average (SLOB)

12.11 Total power quotient (TPQ)

12.12 Modified weighted pitcher’s rating (MWPR)

12.13 Pitching linear weights runs (PLWTS)

12.14 Walks plus hits per innings pitched (WHIP)

Appendix: A word on technology

Answers and hints to selected problems

## Details

- No. of pages:
- 512

- Language:
- English

- Copyright:
- © Academic Press 2021

- Published:
- 18th February 2020

- Imprint:
- Academic Press

- eBook ISBN:
- 9780128184202

- Paperback ISBN:
- 9780128184196

## About the Authors

### Richard Bronson

Richard Bronson has written several books and numerous articles on Mathematics. He has served as Interim Provost of the Metropolitan Campus, and has been Acting Dean of the College of Science and Engineering at the university in New Jersey.

### Affiliations and Expertise

Richard Bronson is a Professor of Mathematics and Computer Science at Fairleigh Dickinson University and is Senior Executive Assistant to the President. Ph.D., in Mathematics from Stevens Institute of Technology.

### Gabriel Costa

Gabriel B. Costa is currently a visiting professor at the United States Military Academy at West Point and is on the faculty at Seton Hall. And is an engineer. He holds many titles and fills them with distinction. He has a B.S., M.S. and Ph.D. in Mathematics from Stevens Institute of Technology. He pioneered one of the first courses in Sabermetrics at West Point, and he has also co-authored two other Academic Press books with Richard Bronson, Matrix Methods, Third Edition, as well as with John T. Saccoman, Linear Algebra: Algorithms, Applications, and Techniques, Third Edition.

### Affiliations and Expertise

Department of Mathematical Sciences, United States Military Academy, West Point, NY, USA