Gamma matricesIn mathematical physics, the gamma matrices, also called the Dirac matrices, are a set of conventional matrices with specific anticommutation relations that ensure they generate a matrix representation of the Clifford algebra It is also possible to define higher-dimensional gamma matrices. When interpreted as the matrices of the action of a set of orthogonal basis vectors for contravariant vectors in Minkowski space, the column vectors on which the matrices act become a space of spinors, on which the Clifford algebra of spacetime acts.
Inverse elementIn mathematics, the concept of an inverse element generalises the concepts of opposite (−x) and reciprocal (1/x) of numbers. Given an operation denoted here ∗, and an identity element denoted e, if x ∗ y = e, one says that x is a left inverse of y, and that y is a right inverse of x. (An identity element is an element such that x * e = x and e * y = y for all x and y for which the left-hand sides are defined.
Adjugate matrixIn linear algebra, the adjugate or classical adjoint of a square matrix A is the transpose of its cofactor matrix and is denoted by adj(A). It is also occasionally known as adjunct matrix, or "adjoint", though the latter term today normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose. The product of a matrix with its adjugate gives a diagonal matrix (entries not on the main diagonal are zero) whose diagonal entries are the determinant of the original matrix: where I is the identity matrix of the same size as A.
Higher-dimensional gamma matricesIn mathematical physics, higher-dimensional gamma matrices generalize to arbitrary dimension the four-dimensional Gamma matrices of Dirac, which are a mainstay of relativistic quantum mechanics. They are utilized in relativistically invariant wave equations for fermions (such as spinors) in arbitrary space-time dimensions, notably in string theory and supergravity. The Weyl–Brauer matrices provide an explicit construction of higher-dimensional gamma matrices for Weyl spinors.
General linear groupIn mathematics, the general linear group of degree n is the set of n×n invertible matrices, together with the operation of ordinary matrix multiplication. This forms a group, because the product of two invertible matrices is again invertible, and the inverse of an invertible matrix is invertible, with identity matrix as the identity element of the group. The group is so named because the columns (and also the rows) of an invertible matrix are linearly independent, hence the vectors/points they define are in general linear position, and matrices in the general linear group take points in general linear position to points in general linear position.
LausanneLausanne (loʊˈzæn , USalsoloʊˈzɑːn , lɔzan; Losena lɔˈzəna) is the capital and largest city of the Swiss French-speaking canton of Vaud. It is a hilly city situated on the shores of Lake Geneva, about halfway between the Jura Mountains and the Alps, and facing the French town of Évian-les-Bains across the lake. Lausanne is located northeast of Geneva, the nearest major city. The municipality of Lausanne has a population of about 140,000, making it the fourth largest city in Switzerland after Basel, Geneva, and Zurich, with the entire agglomeration area having about 420,000 inhabitants (as of January 2019).
Lausanne DistrictLausanne District (District de Lausanne) is a district in the canton of Vaud, Switzerland. The seat of the district is the city of Lausanne. Lausanne has an area, , of . Of this area, or 27.3% is used for agricultural purposes, while or 30.9% is forested. Of the rest of the land, or 41.6% is settled (buildings or roads) and or 0.1% is unproductive land. Lausanne has a population () of . Most of the population () speaks French (159,559 or 79.6%), with German being second most common (8,534 or 4.
TriangleA triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted . In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane.
Cheseaux-sur-LausanneCheseaux-sur-Lausanne (ʃəzo syʁ lɔzan, literally Cheseaux on Lausanne; Chesâls) is a municipality in the district of Lausanne in the canton of Vaud in Switzerland. It is a suburb of the city of Lausanne. Cheseaux-sur-Lausanne is first mentioned in 1228 as Chesaus. Cheseaux-sur-Lausanne has an area, , of . Of this area, or 60.3% is used for agricultural purposes, while or 14.6% is forested. Of the rest of the land, or 24.0% is settled (buildings or roads), or 0.7% is either rivers or lakes.
Romanel-sur-LausanneRomanel-sur-Lausanne (ʁɔmanɛl syʁ lɔzan, literally Romanel on Lausanne; Romanél) is a municipality in the canton of Vaud in Switzerland, located in the district of Lausanne. Romanel-sur-Lausanne is first mentioned in 1184 as Romanes. Romanel-sur-Lausanne has an area, , of (depending on calculation method). Of this area, or 59.7% is used for agricultural purposes, while or 3.8% is forested. Of the rest of the land, or 37.8% is settled (buildings or roads). Of the built up area, industrial buildings made up 5.
Belmont-sur-LausanneBelmont-sur-Lausanne (bɛlmɔ̃ syʁ lɔzan, literally Belmont on Lausanne) is a municipality in the district of Lavaux-Oron in the canton of Vaud in Switzerland. It is a suburb of the city of Lausanne. Belmont-sur-Lausanne is first mentioned in 1228 as Belmunt sowie apud bellum Montem. Belmont-sur-Lausanne has an area, , of . Of this area, or 35.1% is used for agricultural purposes, while or 29.8% is forested. Of the rest of the land, or 33.2% is settled (buildings or roads). Of the built up area, housing and buildings made up 23.
Le Mont-sur-LausanneLe Mont-sur-Lausanne (lə mɔ̃ syʁ lɔzan, literally Le Mont on Lausanne; Lo Mont) is a municipality in the district of Lausanne in the canton of Vaud in Switzerland. It is a suburb of the city of Lausanne. Le Mont-sur-Lausanne is first mentioned in 1237 as Monte super Lausannam. Le Mont-sur-Lausanne has an area, , of (depending on calculation method). Of this area, or 51.0% is used for agricultural purposes, while or 18.2% is forested. Of the rest of the land, or 30.0% is settled (buildings or roads).
