Spinors and Minkowski Space

2020 ◽  
pp. 37-52
Author(s):  
Daniel Canarutto
Keyword(s):  
Vector Space ◽  
Minkowski Space ◽  
Dimensional Vector ◽  
Algebraic Structures ◽  
Dimensional Vector Space ◽  
Spacetime Geometry ◽  
Intrinsic Form ◽  
Spinor Geometry ◽  
Original Approach

A partly original approach to spinor geometry, showing how a 2-dimensional vector space, without any further assumpions, generates by natural constructions the fundamental algebraic structures needed to deal with spacetime geometry and particles with spin. Several related notions are expressed in a concise, intrinsic form.

The genus of graphs associated with vector spaces

2019 ◽  
Vol 19 (05) ◽  
pp. 2050086 ◽  
Author(s):  
T. Tamizh Chelvam ◽  
K. Prabha Ananthi
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Undirected Graph ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Vertex Connectivity ◽  
Dimensional Vector Space ◽  
Nonzero Component ◽  
Vertex Set ◽  
Component Graph

Let [Formula: see text] be a k-dimensional vector space over a finite field [Formula: see text] with a basis [Formula: see text]. The nonzero component graph of [Formula: see text], denoted by [Formula: see text], is a simple undirected graph with vertex set as nonzero vectors of [Formula: see text] such that there is an edge between two distinct vertices [Formula: see text] if and only if there exists at least one [Formula: see text] along which both [Formula: see text] and [Formula: see text] have nonzero scalars. In this paper, we find the vertex connectivity and girth of [Formula: see text]. We also characterize all vector spaces [Formula: see text] for which [Formula: see text] has genus either 0 or 1 or 2.

Linear Transformations in n-Dimensional Vector Space. An Introduction to the Theory of Hilbert Space

1953 ◽  
Vol 37 (320) ◽  
pp. 156
Author(s):  
J. L. B. Copper ◽  
H. L. Hamburger ◽  
M. E. Grimshaw
Keyword(s):  
Hilbert Space ◽  
Vector Space ◽  
Dimensional Vector ◽  
Linear Transformations ◽  
Dimensional Vector Space

Algebraically nonequivalent constructivization for infinite-dimensional vector space

1990 ◽  
Vol 29 (6) ◽  
pp. 430-440 ◽  
Author(s):  
D. V. Lytkina
Keyword(s):  
Vector Space ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Infinite Dimensional

scholarly journals THE INVARIANTS FIELD OF SOME FINITE PROJECTIVE LINEAR GROUP ACTIONS

2011 ◽  
Vol 85 (1) ◽  
pp. 19-25
Author(s):  
YIN CHEN
Keyword(s):  
Finite Field ◽  
Projective Space ◽  
Vector Space ◽  
Orthogonal Group ◽  
Homogeneous Polynomial ◽  
Classical Group ◽  
Projective Group ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Projective Linear Group

AbstractLet Fq be a finite field with q elements, V an n-dimensional vector space over Fq and 𝒱 the projective space associated to V. Let G≤GLn(Fq) be a classical group and PG be the corresponding projective group. In this note we prove that if Fq (V )G is purely transcendental over Fq with homogeneous polynomial generators, then Fq (𝒱)PG is also purely transcendental over Fq. We compute explicitly the generators of Fq (𝒱)PG when G is the symplectic, unitary or orthogonal group.

scholarly journals Identities Generalizing the Theorems of Pappus and Desargues

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1382
Author(s):  
Roger D. Maddux
Keyword(s):  
Projective Plane ◽  
Vector Space ◽  
Invariant Theory ◽  
Lattice Theory ◽  
Three Dimensional ◽  
Dimensional Vector ◽  
Dimensional Vector Space

The Theorems of Pappus and Desargues (for the projective plane over a field) are generalized here by two identities involving determinants and cross products. These identities are proved to hold in the three-dimensional vector space over a field. They are closely related to the Arguesian identity in lattice theory and to Cayley-Grassmann identities in invariant theory.

scholarly journals Sets of idempotents that generate the semigroup of singular endomorphisms of a finite-dimensional vector space

1982 ◽  
Vol 25 (2) ◽  
pp. 133-139 ◽  
Author(s):  
R. J. H. Dawlings
Keyword(s):  
Vector Space ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Finite Dimensional Vector Space ◽  
Finite Dimensional ◽  
Mathematical System

IfMis a mathematical system and EndMis the set of singular endomorphisms ofM, then EndMforms a semigroup under composition of mappings. A number of papers have been written to determine the subsemigroupSMof EndMgenerated by the idempotentsEMof EndMfor different systemsM. The first of these was by J. M. Howie [4]; here the case ofMbeing an unstructured setXwas considered. Howie showed that ifXis finite, then EndX=Sx.

scholarly journals Sums of three quadratic endomorphisms of an infinite-dimensional vector space

2017 ◽  
Vol 83 (12) ◽  
pp. 83-111 ◽  
Author(s):  
Clément de Seguins Pazzis
Keyword(s):  
Vector Space ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Infinite Dimensional
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