# Basics of matrix algebra for statistics with R (Record no. 202535)

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000 -LEADER | |
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fixed length control field | 04433cam a2200205 i 4500 |

008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |

fixed length control field | 150812s2016 flua b 001 0 eng |

020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |

International Standard Book Number | 9781498712361 |

082 00 - DEWEY DECIMAL CLASSIFICATION NUMBER | |

Classification number | 519.5028553 |

Item number | F4B2 |

100 1# - MAIN ENTRY--PERSONAL NAME | |

Personal name | Fieller, Nick |

9 (RLIN) | 329894 |

245 10 - TITLE STATEMENT | |

Title | Basics of matrix algebra for statistics with R |

260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |

Name of publisher, distributor, etc | CRC Press |

Date of publication, distribution, etc | 2016 |

Place of publication, distribution, etc | Boca Raton |

300 ## - PHYSICAL DESCRIPTION | |

Extent | xviii, 226 p. |

440 ## - SERIES STATEMENT/ADDED ENTRY--TITLE | |

Title | Chapman & Hall/CRC The R series |

9 (RLIN) | 329899 |

504 ## - BIBLIOGRAPHY, ETC. NOTE | |

Bibliography, etc | Table of Contents: Introduction • Objectives • Further Reading • Guide to Notation • An Outline Guide to R • Inputting Data to R • Summary of Matrix Operators in R • Examples of R Commands Vectors and Matrices • Vectors • Matrices • Matrix Arithmetic • Transpose and Trace of Sums and Products • Special Matrices • Partitioned Matrices • Algebraic Manipulation of matrices • Useful Tricks • Linear and Quadratic Forms • Creating Matrices in R • Matrix Arithmetic in R • Initial Statistical Applications Rank of Matrices • Introduction and Definitions • Rank Factorization • Rank Inequalities • Rank in Statistics Determinants • Introduction and Definitions • Implementation in R • Properties of Determinants • Orthogonal Matrices • Determinants of Partitioned Matrices • A Key Property of Determinants Inverses • Introduction and Definitions • Properties • Implementation in R • Inverses of Patterned Matrices • Inverses of Partitioned Matrices • General Formulae • Initial Applications Continued Eigenanalysis of Real Symmetric Matrices • Introduction and Definitions • Eigenvectors • Implementation in R • Properties of Eigenanalyses • A Key Statistical Application: PCA • Matrix Exponential • Decompositions • Eigenanalysis of Matrices with Special Structures • Summary of Key Results Vector and Matrix Calculus • Introduction • Differentiation of a Scalar with Respect to a Vector • Differentiation of a Scalar with Respect to a Matrix • Differentiation of a Vector with Respect to a Vector • Differentiation of a Matrix with Respect to a Scalar • Use of Eigenanalysis in Constrained Optimization Further Topics • Introduction • Further Matrix Decompositions • Generalized Inverses • Hadamard Products • Kronecker Products and the Vec Operator Key Applications to Statistics • Introduction • The Multivariate Normal Distribution • Principal Component Analysis • Linear Discriminant Analysis • Canonical Correlation Analysis • Classical Scaling • Linear Models Outline Solutions to Exercises |

520 ## - SUMMARY, ETC. | |

Summary, etc | Basics of Matrix Algebra for Statistics with R provides a guide to elementary matrix algebra sufficient for undertaking specialized courses, such as multivariate data analysis and linear models. It also covers advanced topics, such as generalized inverses of singular and rectangular matrices and manipulation of partitioned matrices, for those who want to delve deeper into the subject. The book introduces the definition of a matrix and the basic rules of addition, subtraction, multiplication, and inversion. Later topics include determinants, calculation of eigenvectors and eigenvalues, and differentiation of linear and quadratic forms with respect to vectors. The text explores how these concepts arise in statistical techniques, including principal component analysis, canonical correlation analysis, and linear modeling. In addition to the algebraic manipulation of matrices, the book presents numerical examples that illustrate how to perform calculations by hand and using R. Many theoretical and numerical exercises of varying levels of difficulty aid readers in assessing their knowledge of the material. Outline solutions at the back of the book enable readers to verify the techniques required and obtain numerical answers. Avoiding vector spaces and other advanced mathematics, this book shows how to manipulate matrices and perform numerical calculations in R. It prepares readers for higher-level and specialized studies in statistics. (https://www.crcpress.com/Basics-of-Matrix-Algebra-for-Statistics-with-R/Fieller/9781498712361) |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Mathematical statistics - Data processing |

9 (RLIN) | 329895 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | Matrices - Data processing |

9 (RLIN) | 329896 |

650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |

Topical term or geographic name as entry element | R (Computer program language) |

9 (RLIN) | 329897 |

942 ## - ADDED ENTRY ELEMENTS (KOHA) | |

Source of classification or shelving scheme | |

Item type | Books |

Withdrawn status | Lost status | Source of classification or shelving scheme | Damaged status | Not for loan | Collection code | Permanent location | Current location | Shelving location | Date acquired | Source of acquisition | Cost, normal purchase price | Total Checkouts | Total Renewals | Full call number | Barcode | Checked out | Date last seen | Date last borrowed | Cost, replacement price | Koha item type |
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Non-fiction | Vikram Sarabhai Library | Vikram Sarabhai Library | General Stacks | 2016-02-16 | Astha Book Agency | 3203.42 | 2 | 2 | 519.5028553 F4B2 | 191146 | 2019-10-03 | 2018-11-06 | 2018-11-06 | 4004.27 | Books |