Includes bibliographical references and index.

"A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm's mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to answer important questions like these is to analyze the spatial and temporal characteristics--origin, rates, and frequencies--of these phenomena. This comprehensive text introduces advanced undergraduate students, graduate students, and researchers to the statistical and algebraic methods used to analyze spatiotemporal data in a range of fields, including climate science, geophysics, ecology, astrophysics, and medicine. Gidon Eshel begins with a concise yet detailed primer on linear algebra, providing readers with the mathematical foundations needed for data analysis. He then fully explains the theory and methods for analyzing spatiotemporal data, guiding readers from the basics to the most advanced applications. This self-contained, practical guide to the analysis of multidimensional data sets features a wealth of real-world examples as well as sample homework exercises and suggested exams"-- Machine generated contents note: One.Introduction and Motivation -- Two.Notation and Basic Operations -- Three.Matrix Properties, Fundamental Spaces, Orthogonality -- 3.1.Vector Spaces -- 3.2.Matrix Rank -- 3.3.Fundamental Spaces Associated with A Element of R^MxN -- 3.4.Gram-Schmidt Orthogonalization -- 3.5.Summary -- Four.Introduction to Eigenanalysis -- 4.1.Preface -- 4.2.Eigenanalysis Introduced -- 4.3.Eigenanalysis as Spectral Representation -- 4.4.Summary -- Five.The Algebraic Operation of SVD -- 5.1.SVD Introduced -- 5.2.Some Examples -- 5.3.SVD Applications -- 5.4.Summary -- Six.The Gray World of Practical Data Analysis: An Introduction to Part 2 -- Seven.Statistics in Deterministic Sciences: An Introduction -- 7.1.Probability Distributions -- 7.2.Degrees of Freedom -- Eight.Autocorrelation -- 8.1.Theoretical Autocovariance and Autocorrelation Functions of AR(1) and AR(2) -- 8.2.Acf-derived Timescale -- 8.3.Summary of Chapters 7 and 8 -- Nine.Regression And Least Squares -- 9.1.Prologue -- 9.2.Setting Up the Problem -- 9.3.The Linear System Ax = b -- 9.4.Least Squares: The SVD View -- 9.5.Some Special Problems Giving Rise to Linear Systems -- 9.6.Statistical Issues in Regression Analysis -- 9.7.Multidimensional Regression and Linear Model Identification -- 9.8.Summary -- Ten.The Fundamental Theorem Of Linear Algebra -- 10.1.Introduction -- 10.2.The Forward Problem -- 10.3.The Inverse Problem -- Eleven.Empirical Orthogonal Functions -- 11.1.Introduction -- 11.2.Data Matrix Structure Convention -- 11.3.Reshaping Multidimensional Data Sets for EOF Analysis -- 11.4.Forming Anomalies and Removing Time Mean -- 11.5.Missing Values, Take 1 -- 11.6.Choosing and Interpreting the Covariability Matrix -- 11.7.Calculating the EOFs -- 11.8.Missing Values, Take 2 -- 11.9.Projection Time Series, the Principal Components -- 11.10.A Final Realistic and Slightly Elaborate Example: Southern New York State Land Surface Temperature -- 11.11.Extended EOF Analysis, EEOF -- 11.12.Summary -- Twelve.The Svd Analysis Of Two Fields -- 12.1.A Synthetic Example -- 12.2.A Second Synthetic Example -- 12.3.A Real Data Example -- 12.4.EOFs as a Prefilter to SVD -- 12.5.Summary -- Thirteen.Suggested Homework -- 13.1.Homework 1, Corresponding to Chapter 3 -- 13.2.Homework 2, Corresponding to Chapter 3 -- 13.3.Homework 3, Corresponding to Chapter 3 -- 13.4.Homework 4, Corresponding to Chapter 4 -- 13.5.Homework 5, Corresponding to Chapter 5 -- 13.6.Homework 6, Corresponding to Chapter 8 -- 13.7.A Suggested Midterm Exam -- 13.8.A Suggested Final Exam.