Basic Properties of Matrices

  • James E. Gentle
Part of the Springer Texts in Statistics book series (STS)


In this chapter, we build on the notions introduced on page 5, and discuss a wide range of basic topics related to matrices with real elements. Some of the properties carry over to matrices with complex elements, but the reader should not assume this. Occasionally, for emphasis, we will refer to “real” matrices, but unless it is stated otherwise, we are assuming the matrices are real.


  1. Campbell, S. L., and C. D. Meyer, Jr. 1991. Generalized Inverses of Linear Transformations. New York: Dover Publications, Inc.zbMATHGoogle Scholar
  2. Carmeli, Moshe. 1983. Statistical Theory and Random Matrices. New York: Marcel Dekker, Inc.zbMATHGoogle Scholar
  3. Eckart, Carl, and Gale Young. 1936. The approximation of one matrix by another of lower rank. Psychometrika 1:211–218.CrossRefzbMATHGoogle Scholar
  4. Harville, David A. 1997. Matrix Algebra from a Statistician’s Point of View. New York: Springer-Verlag.CrossRefzbMATHGoogle Scholar
  5. Horn, Roger A., and Charles R. Johnson. 1991. Topics in Matrix Analysis. Cambridge, United Kingdom: Cambridge University Press.CrossRefzbMATHGoogle Scholar
  6. Kollo, Tõnu, and Dietrich von Rosen. 2005. Advanced Multivariate Statistics with Matrices. Amsterdam: Springer.CrossRefzbMATHGoogle Scholar
  7. Moore, E. H. 1920. On the reciprocal of the general algebraic matrix. Bulletin of the American Mathematical Society 26:394–395.Google Scholar
  8. Penrose, R. 1955. A generalized inverse for matrices. Proceedings of the Cambridge Philosophical Society 51:406–413.CrossRefzbMATHGoogle Scholar
  9. Searle, Shayle R. 1982. Matrix Algebra Useful for Statistics. New York: John Wiley and Sons.zbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • James E. Gentle
    • 1
  1. 1.FairfaxUSA

Personalised recommendations