Matrix Methods: Applied Linear Algebra and Sabermetrics

Matrix MethodsApplied Linear Algebra and SabermetricsFourth EditionRichard BronsonGabriel B. Costa?
Copyright
Dedications
Preface to the third edition
Preface to the fourth edition
. About the authors
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
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
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
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
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
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
7. Matrix calculus
	7.1 Well-defined functions
	Problems 7.1
	7.2 Cayley–Hamilton theorem
	Problems 7.2
	7.3 Polynomials of matrices—distinct eigenvalues
	Problems 7.3
	7.4 Polynomials of matrices—general 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
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 systems—general case
	Problem 8.5
	8.6 Final comments on Chapter 8
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
10. Real inner products and least squares
	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
11. Sabermetrics – 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
		Sabermetrics – the search for objective knowledge about baseball (Bill James)
			How to do sabermetrics
	11.6 Informal reference list
		(A) Websites
		(B) Books
	11.7 Testing
12. Sabermetrics – 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)
A word on technology
Answers and hints to selected problems
	Chapter 1
		Section 1.1
		Section 1.1
		Section 1.2
		Section 1.2
		Section 1.3
		Section 1.3
		Section 1.4
		Section 1.4
		Section 1.5
		Section 1.5
		Section 1.6
		Section 1.6
		Section 1.7
		Section 1.7
	Chapter 2
		Section 2.1
		Section 2.1
		Section 2.2
		Section 2.2
		Section 2.3
		Section 2.3
		Section 2.4
		Section 2.4
		Section 2.5
		Section 2.5
		Section 2.6
		Section 2.6
		Section 2.7
		Section 2.7
	Chapter 3
		Section 3.1
		Section 3.1
		Section 3.2
		Section 3.2
		Section 3.3
		Section 3.3
		Section 3.4
		Section 3.4
		Section 3.5
		Section 3.5
	Chapter 4
		Section 4.1
		Section 4.1
		Section 4.2
		Section 4.2
		Section 4.3
		Section 4.3
		Section 4.4
		Section 4.4
	Chapter 5
		Section 5.1
		Section 5.1
		Section 5.2
		Section 5.2
		Section 5.3
		Section 5.3
		Section 5.4
		Section 5.4
		Section 5.5
		Section 5.5
		Section 5.6
		Section 5.6
	Chapter 6
		Section 6.1
		Section 6.1
		Section 6.2
		Section 6.2
		Section 6.3
		Section 6.3
		Section 6.4
		Section 6.4
		Section 6.5
		Section 6.5
		Section 6.6
		Section 6.6
	Chapter 7
		Section 7.1
		Section 7.1
		Section 7.2
		Section 7.2
		Section 7.3
		Section 7.3
		Section 7.4
		Section 7.4
		Section 7.5
		Section 7.5
		Section 7.6
		Section 7.6
		Section 7.7
		Section 7.7
		Section 7.8
		Section 7.8
		Section 7.9
		Section 7.9
	Chapter 8
		Section 8.1
		Section 8.1
		Section 8.2
		Section 8.2
		Section 8.3
		Section 8.3
		Section 8.4
		Section 8.4
		Section 8.5
		Section 8.5
	Chapter 9
		Section 9.1
		Section 9.1
		Section 9.2
		Section 9.2
		Section 9.3
		Section 9.3
		Section 9.4
		Section 9.4
	Chapter 10
		Section 10.1
		Section 10.1
		Section 10.2
		Section 10.2
		Section 10.3
		Section 10.3
		Section 10.4
		Section 10.4
		Section 10.5
		Section 10.5
	Chapter 11
	Chapter 12
Index
A
B
C
D
E
F
G
H
I
L
M
N
O
P
Q
R
S
T
U
V
W
Z