Encyclopedia of Operations Research and Management Science

2001 Edition
| Editors: Saul I. Gass, Carl M. Harris

Quadratic form

Reference work entry
DOI: https://doi.org/10.1007/1-4020-0611-X_836

A function that can be written as xvTvCx,v where the n × n matrix Cv is a matrix of known coefficients and xv is a column vector. Matrix Cv is usually assumed to be symmetric or can be transformed into a symmetric martrix. The form is said to be positive definite if xvTvCxv > 0 for xv ≠ 0. The form is positive semidefinite if xvTvCxv ≥ 0 for all x.v Negative definite and negative semidefinite forms are defined by appropriate reversal of the inequality signs in the preceding definitions. Matrices and matrix algebra.

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© Kluwer Academic Publishers 2001

Authors and Affiliations

  1. 1.Robert H. Smith School of BusinessUniversity of MarylandCollege PartUSA
  2. 2.School of Information Technology & EngineeringGeorge Mason UniversityFairfaxUSA