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Matrix Methods
Applied Linear Algebra and Sabermetrics
4th Edition - February 5, 2020
Authors: Richard Bronson, Gabriel B. Costa
Language: English
Paperback ISBN:9780128184196
9 7 8 - 0 - 1 2 - 8 1 8 4 1 9 - 6
eBook ISBN:9780128184202
9 7 8 - 0 - 1 2 - 8 1 8 4 2 0 - 2
Matrix Methods: Applied Linear Algebra and Sabermetrics, Fourth Edition, provides a unique and comprehensive balance between the theory and computation of matrices. Rapid changes i…Read more
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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.
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
Advanced UG and Grad Students in advanced linear algebra, applied linear algebra, and matrix algebra courses
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
6.6 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
No. of pages: 512
Language: English
Edition: 4
Published: February 5, 2020
Imprint: Academic Press
Paperback ISBN: 9780128184196
eBook ISBN: 9780128184202
RB
Richard Bronson
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. He 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
Professor of Mathematics and Computer Science, Senior Executive Assistant to the President, Fairleigh Dickinson University, USA
GC
Gabriel B. 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 has also co-authored another Academic Press book with Richard Bronson, Matrix Methods.
Affiliations and expertise
Visiting Professor, Department of Mathematical Sciences, United States Military Academy, West Point, NY, USA