linear form

Noun

 * 1)  A linear functional.
 * 2) * 1961 [Prentice-Hall], Richard A. Silverman (translator),, An Introduction to the Theory of Linear Spaces, 1974, Dover, page 66,
 * A more general linear form in the same space is the expression
 * $$f(x)=\sum_{k+1}^n {c_k \zeta_k}$$
 * with arbitrary fixed coefficients $$c_1, c_2\dots, c_n$$.
 * with arbitrary fixed coefficients $$c_1, c_2\dots, c_n$$.

Usage notes

 * The terms linear form and are semantically interchangeable. However, the former appears to emphasise that the entity is an algebraic structure, while the latter emphasises that it is a mapping. Thus, linear form is arguably more appropriate to linear algebra, and linear functional to functional analysis.