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.
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.
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.
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.
Matrix decompositionIn the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices. There are many different matrix decompositions; each finds use among a particular class of problems. In numerical analysis, different decompositions are used to implement efficient matrix algorithms. For instance, when solving a system of linear equations , the matrix A can be decomposed via the LU decomposition.
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.
Matrix ringIn abstract algebra, a matrix ring is a set of matrices with entries in a ring R that form a ring under matrix addition and matrix multiplication . The set of all n × n matrices with entries in R is a matrix ring denoted Mn(R) (alternative notations: Matn(R) and Rn×n). Some sets of infinite matrices form infinite matrix rings. Any subring of a matrix ring is a matrix ring. Over a rng, one can form matrix rngs. When R is a commutative ring, the matrix ring Mn(R) is an associative algebra over R, and may be called a matrix algebra.
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.
