Null vector, the Glossary

Table of Contents

1. 36 relations: Academic Press, Basis (linear algebra), Bicomplex number, Bilinear form, Bioctonion, Biquaternion, Cambridge University Press, Cayley–Dickson construction, Communications in Mathematical Physics, Complex number, Composition algebra, Definite quadratic form, Division algebra, Emil Artin, Geometric Algebra (book), Imaginary unit, Isotropic line, Isotropic quadratic form, Leonard Eugene Dickson, Lie algebra, Linear independence, Mathematics, Minkowski space, Newman–Penrose formalism, Orthogonality, Project Euclid, Pseudo-Euclidean space, Quadratic form, Real number, Spacetime, Spacetime topology, Split-complex number, Split-octonion, Split-quaternion, Vector space, Verma module.

Academic Press

Academic Press (AP) is an academic book publisher founded in 1941.

See Null vector and Academic Press

Basis (linear algebra)

In mathematics, a set of vectors in a vector space is called a basis (bases) if every element of may be written in a unique way as a finite linear combination of elements of. Null vector and basis (linear algebra) are linear algebra.

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Bicomplex number

In abstract algebra, a bicomplex number is a pair of complex numbers constructed by the Cayley–Dickson process that defines the bicomplex conjugate (w,z)^*.

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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). Null vector and bilinear form are linear algebra.

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Bioctonion

In mathematics, a bioctonion, or complex octonion, is a pair (p,q) where p and q are biquaternions.

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Biquaternion

In abstract algebra, the biquaternions are the numbers, where, and are complex numbers, or variants thereof, and the elements of multiply as in the quaternion group and commute with their coefficients.

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Cambridge University Press

Cambridge University Press is the university press of the University of Cambridge.

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Cayley–Dickson construction

In mathematics, the Cayley–Dickson construction, named after Arthur Cayley and Leonard Eugene Dickson, produces a sequence of algebras over the field of real numbers, each with twice the dimension of the previous one.

See Null vector and Cayley–Dickson construction

Communications in Mathematical Physics

Communications in Mathematical Physics is a peer-reviewed academic journal published by Springer.

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Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.

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Composition algebra

In mathematics, a composition algebra over a field is a not necessarily associative algebra over together with a nondegenerate quadratic form that satisfies for all and in. Null vector and composition algebra are quadratic forms.

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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 non-zero vector of. Null vector and definite quadratic form are linear algebra and quadratic forms.

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Division algebra

In the field of mathematics called abstract algebra, a division algebra is, roughly speaking, an algebra over a field in which division, except by zero, is always possible.

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Emil Artin

Emil Artin (March 3, 1898 – December 20, 1962) was an Austrian mathematician of Armenian descent.

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Geometric Algebra (book)

Geometric Algebra is a book written by Emil Artin and published by Interscience Publishers, New York, in 1957.

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Imaginary unit

The imaginary unit or unit imaginary number is a solution to the quadratic equation Although there is no real number with this property, can be used to extend the real numbers to what are called complex numbers, using addition and multiplication.

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Isotropic line

In the geometry of quadratic forms, an isotropic line or null line is a line for which the quadratic form applied to the displacement vector between any pair of its points is zero. Null vector and isotropic line are quadratic forms.

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Isotropic quadratic form

In mathematics, a quadratic form over a field F is said to be isotropic if there is a non-zero vector on which the form evaluates to zero. Null vector and isotropic quadratic form are quadratic forms.

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Leonard Eugene Dickson

Leonard Eugene Dickson (January 22, 1874 – January 17, 1954) was an American mathematician.

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Lie algebra

In mathematics, a Lie algebra (pronounced) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity.

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Linear independence

In the theory of vector spaces, a set of vectors is said to be if there exists no nontrivial linear combination of the vectors that equals the zero vector. Null vector and linear independence are linear algebra.

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Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

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Minkowski space

In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation.

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Newman–Penrose formalism

The Newman–Penrose (NP) formalism The original paper by Newman and Penrose, which introduces the formalism, and uses it to derive example results.

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Orthogonality

In mathematics, orthogonality is the generalization of the geometric notion of perpendicularity.

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Project Euclid

Project Euclid is a collaborative partnership between Cornell University Library and Duke University Press which seeks to advance scholarly communication in theoretical and applied mathematics and statistics through partnerships with independent and society publishers.

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Pseudo-Euclidean space

In mathematics and theoretical physics, a pseudo-Euclidean space of signature is a finite-dimensional ''n''-space together with a non-degenerate quadratic form.

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Quadratic form

In mathematics, a quadratic form is a polynomial with terms all of degree two ("form" is another name for a homogeneous polynomial). Null vector and quadratic form are linear algebra and quadratic forms.

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Real number

In mathematics, a real number is a number that can be used to measure a continuous one-dimensional quantity such as a distance, duration or temperature.

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Spacetime

In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum.

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Spacetime topology

Spacetime topology is the topological structure of spacetime, a topic studied primarily in general relativity.

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Split-complex number

In algebra, a split complex number (or hyperbolic number, also perplex number, double number) is based on a hyperbolic unit satisfying j^2. Null vector and split-complex number are linear algebra.

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Split-octonion

In mathematics, the split-octonions are an 8-dimensional nonassociative algebra over the real numbers.

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Split-quaternion

In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name.

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Vector space

In mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called ''vectors'', can be added together and multiplied ("scaled") by numbers called ''scalars''.

See Null vector and Vector space

Verma module

Verma modules, named after Daya-Nand Verma, are objects in the representation theory of Lie algebras, a branch of mathematics.

See Null vector and Verma module

References

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

Also known as Anisotropic quadratic space, Isotropic cone, Isotropic vector, Non-zero vector, Null cone, Null vector (vector space), Null vectors, Split algebra.