In
mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, 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 linea ...
or a
sesquilinear form may be naturally associated, which is
positive-definite In mathematics, positive definiteness is a property of any object to which a bilinear form or a sesquilinear form may be naturally associated, which is positive-definite. See, in particular:
* Positive-definite bilinear form
* 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.
Definition 1
Let \mathbb be the set of real numbers and \mathbb be the set of complex numbers.
A function f: \mathbb \to \mathbb is ...
*
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 \mathbf^\mathsf M \mathbf is positive for every nonzero real column vector \mathbf, where \mathbf^\mathsf is the row vector transpose of \mathbf.
Mo ...
*
Positive-definite operator
*
Positive-definite quadratic form
References
*.
*.
{{Set index article, mathematics
Quadratic forms