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Positive definiteness

Index Positive definiteness

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. [1]

8 relations: Bilinear form, Definite quadratic form, Mathematics, Positive-definite function, Positive-definite function on a group, Positive-definite kernel, Positive-definite matrix, Sesquilinear form.

Bilinear form

In mathematics, more specifically in abstract algebra and linear algebra, a bilinear form on a vector space V is a bilinear map, where K is the field of scalars.

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Definite quadratic form

In mathematics, a definite quadratic form is a quadratic form over some real vector space that has the same sign (always positive or always negative) for every nonzero vector of.

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Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

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Positive-definite function

In mathematics, a positive-definite function is, depending on the context, either of two types of function.

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Positive-definite function on a group

In mathematics, and specifically in operator theory, a positive-definite function on a group relates the notions of positivity, in the context of Hilbert spaces, and algebraic groups.

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Positive-definite kernel

In operator theory, a branch of mathematics, a positive definite kernel is a generalization of a positive definite function or a positive-definite matrix.

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Positive-definite matrix

In linear algebra, a symmetric real matrix M is said to be positive definite if the scalar z^Mz is strictly positive for every non-zero column vector z of n real numbers.

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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.

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Redirects here:

Positive definite, Positive definiteness (disambiguation), Positive-definite.

References

[1] https://en.wikipedia.org/wiki/Positive_definiteness

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