In mathematics, positive definiteness is a property of any object to which a

bilinear form In mathematics, a bilinear form is a bilinear map on a vector space (the elements of which are called '' vectors'') over a field ''K'' (the elements of which are called '' scalars''). In other words, a bilinear form is a function that is lin ...

or a

sesquilinear form In mathematics, a sesquilinear form is a generalization of a bilinear form that, in turn, is a generalization of the concept of the dot product of Euclidean space. A bilinear form is linear in each of its arguments, but a sesquilinear form allows ...

may be naturally associated, which is positive-definite. See, in particular: * Positive-definite bilinear form *

Positive-definite function In mathematics, a positive-definite function is, depending on the context, either of two types of function. Most common usage A ''positive-definite function'' of a real variable ''x'' is a complex-valued function f: \mathbb \to \mathbb suc ...

* Positive-definite function on a group * Positive-definite functional * Positive-definite kernel *

Positive-definite matrix In mathematics, a symmetric matrix M with real entries is positive-definite if the real number z^\textsfMz is positive for every nonzero real column vector z, where z^\textsf is the transpose of More generally, a Hermitian matrix (that is, ...

* Positive-definite quadratic form

References

*. *. {{Set index article, mathematics Quadratic forms