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Linear Algebra and Matrix Analysis for Statistics

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1 Matrices, Vectors and Their Operations 1 1.1 Basic definitions and notations 2 1.2 Matrix addition and scalar-matrix multiplication 5 1.3 Matrix multiplication 7 1.4 Partitioned matrices 14 1.4.1 2  2 partitioned matrices 14 1.4.2 General partitioned matrices 16 1.5 The “trace” of a square matrix 18 1.6 Some special matrices 20 1.6.1 Permutation matrices 20 1.6.2 Triangular matrices 22 1.6.3 Hessenberg matrices 24 1.6.4 Sparse matrices 26 1.6.5 Banded matrices 27 1.7 Exercises 29 2 Systems of Linear Equations 33 2.1 Introduction 33 2.2 Gaussian elimination 34 2.3 Gauss-Jordan elimination 42 2.4 Elementary matrices 44 2.5 Homogeneous linear systems 48 2.6 The inverse of a matrix 51 2.7 Exercises 61 ix1 Matrices, Vectors and Their Operations 1 1.1 Basic definitions and notations 2 1.2 Matrix addition and scalar-matrix multiplication 5 1.3 Matrix multiplication 7 1.4 Partitioned matrices 14 1.4.1 2  2 partitioned matrices 14 1.4.2 General partitioned matrices 16 1.5 The “trace” of a square matrix 18 1.6 Some special matrices 20 1.6.1 Permutation matrices 20 1.6.2 Triangular matrices 22 1.6.3 Hessenberg matrices 24 1.6.4 Sparse matrices 26 1.6.5 Banded matrices 27 1.7 Exercises 29 2 Systems of Linear Equations 33 2.1 Introduction 33 2.2 Gaussian elimination 34 2.3 Gauss-Jordan elimination 42 2.4 Elementary matrices 44 2.5 Homogeneous linear systems 48 2.6 The inverse of a matrix 51 2.7 Exercises 61 ix

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Texts in Statistical Science



Linear Algebra and
Matrix Analysis for
Statistics




Sudipto Banerjee
Anindya Roy




www.Ebook777.com


5/6/14 1:49 PM

,Free ebooks ==> www.Ebook777.com




Linear Algebra and
Matrix Analysis for
Statistics




www.Ebook777.com

,CHAPMAN & HALL/CRC
Texts in Statistical Science Series
Series Editors
Francesca Dominici, Harvard School of Public Health, USA
Julian J. Faraway, University of Bath, UK
Martin Tanner, Northwestern University, USA
Jim Zidek, University of British Columbia, Canada

Analysis of Failure and Survival Data Data Driven Statistical Methods
P. J. Smith P. Sprent
The Analysis of Time Series: An Introduction, Decision Analysis: A Bayesian Approach
Sixth Edition J.Q. Smith
C. Chatfield Design and Analysis of Experiments with SAS
Applied Bayesian Forecasting and Time Series J. Lawson
Analysis Elementary Applications of Probability Theory,
A. Pole, M. West, and J. Harrison Second Edition
Applied Categorical and Count Data Analysis H.C. Tuckwell
W. Tang, H. He, and X.M. Tu Elements of Simulation
Applied Nonparametric Statistical Methods, B.J.T. Morgan
Fourth Edition
Epidemiology: Study Design and
P. Sprent and N.C. Smeeton
Data Analysis, Third Edition
Applied Statistics: Handbook of GENSTAT M. Woodward
Analyses
Essential Statistics, Fourth Edition
E.J. Snell and H. Simpson D.A.G. Rees
Applied Statistics: Principles and Examples Exercises and Solutions in Statistical Theory
D.R. Cox and E.J. Snell L.L. Kupper, B.H. Neelon, and S.M. O’Brien
Applied Stochastic Modelling, Second Edition Exercises and Solutions in Biostatistical Theory
B.J.T. Morgan L.L. Kupper, B.H. Neelon, and S.M. O’Brien
Bayesian Data Analysis, Third Edition Extending the Linear Model with R:
A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, Generalized Linear, Mixed Effects and
A. Vehtari, and D.B. Rubin Nonparametric Regression Models
J.J. Faraway
Bayesian Ideas and Data Analysis: An
Introduction for Scientists and Statisticians A First Course in Linear Model Theory
R. Christensen, W. Johnson, A. Branscum, N. Ravishanker and D.K. Dey
and T.E. Hanson Generalized Additive Models:
Bayesian Methods for Data Analysis, An Introduction with R
Third Edition S. Wood
B.P. Carlin and T.A. Louis Generalized Linear Mixed Models:
Modern Concepts, Methods and Applications
Beyond ANOVA: Basics of Applied Statistics
W. W. Stroup
R.G. Miller, Jr.
Graphics for Statistics and Data Analysis with R
The BUGS Book: A Practical Introduction to K.J. Keen
Bayesian Analysis
D. Lunn, C. Jackson, N. Best, A. Thomas, and Interpreting Data: A First Course
D. Spiegelhalter in Statistics
A.J.B. Anderson
A Course in Categorical Data Analysis
T. Leonard Introduction to General and Generalized
Linear Models
A Course in Large Sample Theory H. Madsen and P. Thyregod
T.S. Ferguson

, An Introduction to Generalized Multivariate Analysis of Variance and
Linear Models, Third Edition Repeated Measures: A Practical Approach for
A.J. Dobson and A.G. Barnett Behavioural Scientists
Introduction to Multivariate Analysis D.J. Hand and C.C. Taylor
C. Chatfield and A.J. Collins Multivariate Statistics: A Practical Approach
Introduction to Optimization Methods and B. Flury and H. Riedwyl
Their Applications in Statistics Multivariate Survival Analysis and Competing
B.S. Everitt Risks
Introduction to Probability with R M. Crowder
K. Baclawski Nonparametric Methods in Statistics with SAS
Introduction to Randomized Controlled Applications
Clinical Trials, Second Edition O. Korosteleva
J.N.S. Matthews Pólya Urn Models
Introduction to Statistical Inference and Its H. Mahmoud
Applications with R Practical Data Analysis for Designed
M.W. Trosset Experiments
Introduction to Statistical Limit Theory B.S. Yandell
A.M. Polansky Practical Longitudinal Data Analysis
Introduction to Statistical Methods for D.J. Hand and M. Crowder
Clinical Trials Practical Multivariate Analysis, Fifth Edition
T.D. Cook and D.L. DeMets A. Afifi, S. May, and V.A. Clark
Introduction to Statistical Process Control Practical Statistics for Medical Research
P. Qiu D.G. Altman
Introduction to the Theory of Statistical A Primer on Linear Models
Inference J.F. Monahan
H. Liero and S. Zwanzig Principles of Uncertainty
Large Sample Methods in Statistics J.B. Kadane
P.K. Sen and J. da Motta Singer Probability: Methods and Measurement
Linear Algebra and Matrix Analysis for A. O’Hagan
Statistics Problem Solving: A Statistician’s Guide,
S. Banerjee and A. Roy Second Edition
Logistic Regression Models C. Chatfield
J.M. Hilbe Randomization, Bootstrap and Monte Carlo
Markov Chain Monte Carlo: Methods in Biology, Third Edition
Stochastic Simulation for Bayesian Inference, B.F.J. Manly
Second Edition Readings in Decision Analysis
D. Gamerman and H.F. Lopes S. French
Mathematical Statistics Sampling Methodologies with Applications
K. Knight P.S.R.S. Rao
Modeling and Analysis of Stochastic Systems, Stationary Stochastic Processes: Theory and
Second Edition Applications
V.G. Kulkarni G. Lindgren
Modelling Binary Data, Second Edition Statistical Analysis of Reliability Data
D. Collett M.J. Crowder, A.C. Kimber,
Modelling Survival Data in Medical Research, T.J. Sweeting, and R.L. Smith
Second Edition Statistical Methods for Spatial Data Analysis
D. Collett O. Schabenberger and C.A. Gotway

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