Eigen Matrix Example
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Eigenvalues of Matrices
A comprehensive and accessible guide to the calculation of eigenvalues of matrices, ideal for undergraduates, or researchers/engineers in industry.
Linear Models in Matrix Form
This textbook is an approachable introduction to statistical analysis using matrix algebra. Prior knowledge of matrix algebra is not necessary. Advanced topics are easy to follow through analyses that were performed on an open-source spreadsheet using a few built-in functions. These topics include ordinary linear regression, as well as maximum likelihood estimation, matrix decompositions, nonparametric smoothers and penalized cubic splines. Each data set (1) contains a limited number of observations to encourage readers to do the calculations themselves, and (2) tells a coherent story based on statistical significance and confidence intervals. In this way, students will learn how the numbers were generated and how they can be used to make cogent arguments about everyday matters. This textbook is designed for use in upper level undergraduate courses or first year graduate courses. The first chapter introduces students to linear equations, then covers matrix algebra, focusing on three essential operations: sum of squares, the determinant, and the inverse. These operations are explained in everyday language, and their calculations are demonstrated using concrete examples. The remaining chapters build on these operations, progressing from simple linear regression to mediational models with bootstrapped standard errors.
Computational Analysis and Understanding of Natural Languages: Principles, Methods and Applications
Computational Analysis and Understanding of Natural Languages: Principles, Methods and Applications, Volume 38, the latest release in this monograph that provides a cohesive and integrated exposition of these advances and associated applications, includes new chapters on Linguistics: Core Concepts and Principles, Grammars, Open-Source Libraries, Application Frameworks, Workflow Systems, Mathematical Essentials, Probability, Inference and Prediction Methods, Random Processes, Bayesian Methods, Machine Learning, Artificial Neural Networks for Natural Language Processing, Information Retrieval, Language Core Tasks, Language Understanding Applications, and more. The synergistic confluence of linguistics, statistics, big data, and high-performance computing is the underlying force for the recent and dramatic advances in analyzing and understanding natural languages, hence making this series all the more important. - Provides a thorough treatment of open-source libraries, application frameworks and workflow systems for natural language analysis and understanding - Presents new chapters on Linguistics: Core Concepts and Principles, Grammars, Open-Source Libraries, Application Frameworks, Workflow Systems, Mathematical Essentials, Probability, and more