3. Linear Algebra

  1. Paolo Brandimarte

Published Online: 24 MAY 2011

DOI: 10.1002/9781118023525.ch3

Quantitative Methods: An Introduction for Business Management

Quantitative Methods: An Introduction for Business Management

How to Cite

Brandimarte, P. (2011) Linear Algebra, in Quantitative Methods: An Introduction for Business Management, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118023525.ch3

Publication History

  1. Published Online: 24 MAY 2011
  2. Published Print: 4 APR 2011

ISBN Information

Print ISBN: 9780470496343

Online ISBN: 9781118023525

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Keywords:

  • determinant;
  • eigenvalues;
  • eigenvectors;
  • linear algebra;
  • linear equations;
  • linear spaces;
  • matrix theory;
  • quadratic form;
  • statistics;
  • vectors

Summary

This chapter first presents a simple motivating example related to pricing a financial derivative. A simple binomial valuation model is discussed, which leads to the formulation of a system of linear equations. Then, the chapter deals with linear spaces and linear algebra, which can be considered as a generalization of the algebra of vectors. Another possibly familiar concept from elementary mathematics is the determinant, which is typically taught as a tool to solve systems of linear equations. The last concepts from matrix theory that the author covers are eigenvalues and eigenvectors. They are fundamental, e.g., in data reduction methods for multivariate statistical analysis, like principal component analysis and factor analysis. The chapter also considers quadratic forms, which play a significant role in both statistics and optimization. They are, essentially, the simplest examples of a nonlinear function of multiple variables.

Controlled Vocabulary Terms

binomial distribution; multivariate statistics; quadratic form