In mathematics, a definite quadratic form is a quadratic form over some real vector space V that has the same sign (always positive or always negative) for every nonzero vector of V. According to that sign, the quadratic form is called positive definite or negative definite.
A semidefinite (or semi-definite) quadratic form is defined in the same way, except that "positive" and "negative" are replaced by "not negative" and "not positive", respectively. An indefinite quadratic form is one that takes on both positive and negative values.
More generally, the definition applies to a vector space over an ordered field.
Read more about Definite Quadratic Form: Associated Symmetric Bilinear Form, Example, See Also
Famous quotes containing the words definite and/or form:
“God is a foreman with certain definite views
Who orders life in shifts of work and leisure.”
—Seamus Heaney (b. 1939)
“One of the many to whom, from straightened circumstances, a consequent inability to form the associations they would wish, and a disinclination to mix with the society they could obtain, London is as complete a solitude as the plains of Syria.”
—Charles Dickens (1812–1870)