Linear Algebra and Linear Models

Framsida
Springer Science & Business Media, 2000 - 138 sidor
1 Recension
The main purpose of Linear Algebra and Linear Modelsis to provide a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing. The necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms are developed along the way. The book is aimed at advanced undergraduate and first-year graduate masters students taking courses in linear algebra, linear models, multivariate analysis, and design of experiments. It should also be of use to research mathematicians and statisticians as a source of standard results and problems.
 

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Innehåll

Vector Spaces and Matrices
1
12 Vector Spaces and Subspaces
4
13 Basis and Dimension
5
14 Rank
8
15 Orthogonality
10
16 Nonsingularity
14
17 Frobenius Inequality
16
18 Eigenvalues and the Spectral Theorem
18
38 Exercises
73
39 Hints and Solutions
76
Singular Values and Their Applications
79
42 Extremal Representations
81
43 Majorization
84
44 Principal Components
86
45 Canonical Correlations
88
46 Volume of a Matrix
89

19 Exercises
22
110 Hints and Solutions
25
Linear Estimation
29
22 Linear Model
33
23 Estimability
35
24 Weighing Designs
38
25 Residual Sum of Squares
40
26 Estimation Subject to Restrictions
42
27 Exercises
46
28 Hints and Solutions
48
Tests of Linear Hypotheses
51
32 Multivariate Normal Distribution
53
33 Quadratic Forms and Cochrans Theorem
57
34 OneWay and TwoWay Classifications
61
35 General Linear Hypothesis
65
36 Extrema of Quadratic Forms
67
37 Multiple Correlation and Regression Models
69
47 Exercises
93
48 Hints and Solutions
94
Block Designs and Optimality
99
52 The CMatrix
102
53 E A and DOptimality
103
54 Exercises
108
55 Hints and Solutions
110
Rank Additivity
112
62 Characterizations of Rank Additivity
114
63 General Linear Model
118
64 The Star Order
122
65 Exercises
124
66 Hints and Solutions
126
Notes
129
References
132
Index
136
Upphovsrätt

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Linear Algebra and Linear Models
Ravindra B. Bapat
Begränsad förhandsgranskning - 2008
Linear Algebra and Linear Models
Ravindra B. Bapat
Ingen förhandsgranskning - 2014
Linear Algebra and Linear Models
R. B. Bapat
Ingen förhandsgranskning - 2000

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Algebra basis BIBD block BLUE Chapter Cochran’s theorem column rank column vector D-optimality defined definition denote dim(S dispersion matrix eigenvalues eigenvector estimable Exercise F-statistic first Frobenius Inequality GA)z given group inverse Hadamard Hadamard inequality hence Hint HintsandSolutions idempotent inequality j)-entry least squares g-inverse Let A,B Let x1 LetA linear combination linear function linear model linear span linearly independent matrices of order matrix and let matrix of rank minimum norm g-inverse model E(y Moore–Penrose inverse multiplicity n×n matrix nonsingular matrix nonzero observations orthogonal matrix orthonormal partitioned positive definite positive semidefinite positive semidefinite matrix principal component principal minors principal submatrix proof is complete R(AB rank factorization real numbers row space Schur complement Similarly singular values solution spectral theorem square matrix star order submatrix subspace Suppose symmetric matrix treatment unbiased variance VC1V vector space vectors x1 zero

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Bibliografisk information

QR code for Linear Algebra and Linear Models
TitelLinear Algebra and Linear Models
Online access with purchase: Springer
Universitext (1979)
Universitext (Berlin. Print)
Universitext - Springer-Verlag
Universitext Series
FörfattareR. B. Bapat
Utgåvaomarbetad
UtgivareSpringer Science & Business Media, 2000
ISBN0387988718, 9780387988719
Längd138 sidor
  
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