linear form

plural linear forms

1. linear algebraA linear functional.

   In #92;mathbb#123;R#125;ⁿ, if vectors are represented as column vectors, then linear forms are represented as row vectors, and their action on vectors is given by the matrix product, with the row vector on the left and the column vector on the right.

   3 more examples

   1961 [Prentice-Hall], Richard A. Silverman (translator), Georgi E. Shilov, An Introduction to the Theory of Linear Spaces, 1974, Dover, page 66, A more general linear form in the same space is the expression f(x)=∑ₖ₊₁ⁿc_kζₖ with arbitrary fixed coefficients c_1,c_2…,c_n.

   In the theory of distributions, functions are replaced by linear forms on an auxiliary vector space, whose members are called test functions.

   1998, F. G. Friedlander, M. Joshi, Introduction to the Theory of Distributions, 2nd edition, Cambridge University Press, page 2

   In order to better understand the effect of reducing a K-vector subspace V#92;subseteqP#95;d modulo a generic linear form, we generalize Proposition 5.5.18 as follows.

   2005, Martin Kreuzer, Lorenzo Robbiano, Computational Commutative Algebra 2, Springer, page 264

   Synonyms: covector, linear functional, one-form