Definite Quadratic Form

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:

    Literature does not exist in a vacuum. Writers as such have a definite social function exactly proportional to their ability as writers. This is their main use.
    Ezra Pound (1885–1972)

    A true poem is distinguished not so much by a felicitous expression, or any thought it suggests, as by the atmosphere which surrounds it. Most have beauty of outline merely, and are striking as the form and bearing of a stranger; but true verses come toward us indistinctly, as the very breath of all friendliness, and envelop us in their spirit and fragrance.
    Henry David Thoreau (1817–1862)