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Matrix Methods - 4th Edition - ISBN: 9780128184196, 9780128184202

Matrix Methods

4th Edition

Applied Linear Algebra and Sabermetrics

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Authors: Richard Bronson Gabriel Costa
eBook ISBN: 9780128184202
Paperback ISBN: 9780128184196
Imprint: Academic Press
Published Date: 18th February 2020
Page Count: 512
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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

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