In mathematics, especially in functional analysis, a positive linear functional on an ordered vector space (V, ≤) is a linear functional f on V so that for all positive elements v of V, that is v≥0, it holds that
In other words, a positive linear functional is guaranteed to take nonnegative values for positive elements. The significance of positive linear functionals lies in results such as Riesz representation theorem.
Read more about Positive Linear Functional: Examples
Famous quotes containing the words positive and/or functional:
“I have always had something to live besides a personal life. And I suspected very early that to live merely in an experience of, in an expression of, in a positive delight in the human cliches could be no business of mine.”
—Margaret Anderson (1886–1973)
“Well designed, fully functional infant. Provides someone to live for as well as another mouth to feed. Produces cooing, gurgling and other adorable sounds. May cause similar behavior in nearby adults. Cries when hungry, sleepy or just because. Hand Wash with warm water and mild soap, then pat dry with soft cloth and talc. Internal mechanisms are self-cleaning... Two Genders: Male. Female. Five Colors: White. Black. Yellow. Red. Camouflage.”
—Alfred Gingold, U.S. humorist. Items From Our Catalogue, “Baby,” Avon Books (1982)