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Inner product space and Pseudo-Riemannian manifold

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Inner product space and Pseudo-Riemannian manifold

Inner product space vs. Pseudo-Riemannian manifold

In linear algebra, an inner product space is a vector space with an additional structure called an inner product. In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

Similarities between Inner product space and Pseudo-Riemannian manifold

Inner product space and Pseudo-Riemannian manifold have 7 things in common (in Unionpedia): Definite quadratic form, Differential geometry, Euclidean space, Minkowski space, Real number, Riemannian manifold, Vector space.

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.

Definite quadratic form and Inner product space · Definite quadratic form and Pseudo-Riemannian manifold · See more »

Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

Differential geometry and Inner product space · Differential geometry and Pseudo-Riemannian manifold · See more »

Euclidean space

In geometry, Euclidean space encompasses the two-dimensional Euclidean plane, the three-dimensional space of Euclidean geometry, and certain other spaces.

Euclidean space and Inner product space · Euclidean space and Pseudo-Riemannian manifold · See more »

Minkowski space

In mathematical physics, Minkowski space (or Minkowski spacetime) is a combining of three-dimensional Euclidean space and time into a four-dimensional manifold where the spacetime interval between any two events is independent of the inertial frame of reference in which they are recorded.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Riemannian manifold

In differential geometry, a (smooth) Riemannian manifold or (smooth) Riemannian space (M,g) is a real, smooth manifold M equipped with an inner product g_p on the tangent space T_pM at each point p that varies smoothly from point to point in the sense that if X and Y are differentiable vector fields on M, then p \mapsto g_p(X(p),Y(p)) is a smooth function.

Inner product space and Riemannian manifold · Pseudo-Riemannian manifold and Riemannian manifold · See more »

Vector space

A vector space (also called a linear space) is a collection of objects called vectors, which may be added together and multiplied ("scaled") by numbers, called scalars.

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The list above answers the following questions

Inner product space and Pseudo-Riemannian manifold Comparison

Inner product space has 106 relations, while Pseudo-Riemannian manifold has 38. As they have in common 7, the Jaccard index is 4.86% = 7 / (106 + 38).

References

This article shows the relationship between Inner product space and Pseudo-Riemannian manifold. To access each article from which the information was extracted, please visit:

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