quadratic form

Noun

quadratic form (plural quadratic forms)

1. A homogeneous polynomial of degree 2 in a given number of variables.
   • Historically, quadratic form theory has been treated as a rich but misunderstood uncle.1980, John Gregory, Quadratic Form Theory and Differential Equations, Academic Press, page ix
   • We claim that this quadratic form is isotropic, and this gives what we need according to [2, Proposition 4.4].2004, Nikita A. Karpenko, Izhboldin's Results on Stably Birational of Equivalence Quadrics, Oleg T. Izhboldin, Geometric Methods in the Algebraic Theory of Quadratic Forms, Springer, Lecture Notes in...
2. (multivariate statistics) A scalar quantity of the form εᵀΛε, where ε is a vector of n random variables, and Λ is an n-dimensional symmetric matrix.
   • Quadratic forms of normal random vectors are of great importance in many branches of statistics, such as least-squares methods, the analysis of variance, regression analysis, and experimental design.2009, Allan Gut, An Intermediate Course in Probability, 2nd edition, Springer, page 136