2. Matrix Algebra

  1. Alvin C. Rencher

Published Online: 27 MAR 2003

DOI: 10.1002/0471271357.ch2

Methods of Multivariate Analysis, Second Edition

Methods of Multivariate Analysis, Second Edition

How to Cite

Rencher, A. C. (2002) Matrix Algebra, in Methods of Multivariate Analysis, Second Edition, John Wiley & Sons, Inc., New York, NY, USA. doi: 10.1002/0471271357.ch2

Author Information

  1. Brigham Young University, USA

Publication History

  1. Published Online: 27 MAR 2003
  2. Published Print: 22 FEB 2002

ISBN Information

Print ISBN: 9780471418894

Online ISBN: 9780471271352



  • matrix;
  • vector;
  • scalar;
  • transpose;
  • matrix equality;
  • symmetric matrix;
  • diagonal matrix;
  • identity matrix;
  • triangular matrix;
  • matrix sum;
  • matrix product;
  • partitioned matrix;
  • rank;
  • inverse;
  • singular matrix;
  • positive definite matrix;
  • Cholesky decomposition;
  • determinant;
  • trace;
  • orthogonal vectors;
  • orthogonal matrix;
  • eigenvalue;
  • eigenvector;
  • spectral decomposition;
  • square root matrix;
  • singular value decomposition


It would be difficult to write a book on multivariate analysis without the compact notation provided by matrix algebra. This chapter introduces all the matrix algebra needed to read the book. A few proofs are given where they seemed instructive, and most techniques are illustrated numerically. A large problem set provides additional numerical illustrations and practice in algebraic manipulations.

The level of presentation does not assume that the reader has had previous exposure to matrix notation, although it would be helpful. Those without prior familiarity with matrices would need to work most of the problems in order to be comfortable with the notation used in the book.