Chapter 2. Basic Concepts in Linear Algebra

  1. André I. Khuri

Published Online: 26 MAR 2003

DOI: 10.1002/0471394882.ch2

Advanced Calculus with Applications in Statistics, Second Edition

Advanced Calculus with Applications in Statistics, Second Edition

How to Cite

Khuri, A. I. (2002) Basic Concepts in Linear Algebra, in Advanced Calculus with Applications in Statistics, Second Edition, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/0471394882.ch2

Author Information

  1. University of Florida, Gainesville, Florida, USA

Publication History

  1. Published Online: 26 MAR 2003
  2. Published Print: 1 NOV 2002

Book Series:

  1. Wiley Series in Probability and Statistics

Book Series Editors:

  1. David J. Balding,
  2. Peter Bloomfield,
  3. Noel A. C. Cressie,
  4. Nicholas I. Fisher,
  5. Iain M. Johnstone,
  6. J. B. Kadane,
  7. Louise M. Ryan,
  8. David W. Scott,
  9. Adrian F. M. Smith and
  10. Jozef L. Teugels

ISBN Information

Print ISBN: 9780471391043

Online ISBN: 9780471394884

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Keywords:

  • balanced mixed model;
  • determinants;
  • diagonalization of matrices;
  • eigenvalues;
  • eigenvectors;
  • extrema of quadratic forms;
  • inverse of a matrix;
  • linear transformation;
  • matrices;
  • singular-value decomposition;
  • vector space

Summary

This chapter covers fundamental concepts concerning vector spaces and matrix algebra, including basic operations on matrices and determinants, the rank of a matrix, description of particular types of matrices, and the diagonalization of matrices. Some applications of matrices in statistics are presented in the last section. This is a brief chapter designed to acquaint the reader with basic matrix terminology that is essential to the understanding of the remaining chapters.