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).
Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
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.
Diagonalizable matrixIn linear algebra, a square matrix is called diagonalizable or non-defective if it is similar to a diagonal matrix, i.e., if there exists an invertible matrix and a diagonal matrix such that , or equivalently . (Such , are not unique.) For a finite-dimensional vector space , a linear map is called diagonalizable if there exists an ordered basis of consisting of eigenvectors of .
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.
DiagonalIn geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge. Informally, any sloping line is called diagonal. The word diagonal derives from the ancient Greek διαγώνιος diagonios, "from angle to angle" (from διά- dia-, "through", "across" and γωνία gonia, "angle", related to gony "knee"); it was used by both Strabo and Euclid to refer to a line connecting two vertices of a rhombus or cuboid, and later adopted into Latin as diagonus ("slanting line").
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.
Genetic disorderA genetic disorder is a health problem caused by one or more abnormalities in the genome. It can be caused by a mutation in a single gene (monogenic) or multiple genes (polygenic) or by a chromosomal abnormality. Although polygenic disorders are the most common, the term is mostly used when discussing disorders with a single genetic cause, either in a gene or chromosome. The mutation responsible can occur spontaneously before embryonic development (a de novo mutation), or it can be inherited from two parents who are carriers of a faulty gene (autosomal recessive inheritance) or from a parent with the disorder (autosomal dominant inheritance).
Main diagonalIn linear algebra, the main diagonal (sometimes principal diagonal, primary diagonal, leading diagonal, major diagonal, or good diagonal) of a matrix is the list of entries where . All off-diagonal elements are zero in a diagonal matrix. The following four matrices have their main diagonals indicated by red ones: Anti-diagonal matrix The antidiagonal (sometimes counter diagonal, secondary diagonal, trailing diagonal, minor diagonal, off diagonal, or bad diagonal) of an order square matrix is the collection of entries such that for all .
Appendix (anatomy)The appendix (: appendices or appendixes; also vermiform appendix; cecal [or caecal] appendix; vermix; or vermiform process) is a finger-like, blind-ended tube connected to the cecum, from which it develops in the embryo. The cecum is a pouch-like structure of the large intestine, located at the junction of the small and the large intestines. The term "vermiform" comes from Latin and means "worm-shaped". The appendix was once considered a vestigial organ, but this view has changed since the early 2000s.
Space diagonalIn geometry, a space diagonal (also interior diagonal or body diagonal) of a polyhedron is a line connecting two vertices that are not on the same face. Space diagonals contrast with face diagonals, which connect vertices on the same face (but not on the same edge) as each other. For example, a pyramid has no space diagonals, while a cube (shown at right) or more generally a parallelepiped has four space diagonals. An axial diagonal is a space diagonal that passes through the center of a polyhedron.
Genetic testingGenetic testing, also known as DNA testing, is used to identify changes in DNA sequence or chromosome structure. Genetic testing can also include measuring the results of genetic changes, such as RNA analysis as an output of gene expression, or through biochemical analysis to measure specific protein output. In a medical setting, genetic testing can be used to diagnose or rule out suspected genetic disorders, predict risks for specific conditions, or gain information that can be used to customize medical treatments based on an individual's genetic makeup.
AppendectomyAn appendectomy (American English), also known as an appendicectomy (British English), is a surgical operation in which the vermiform appendix (a portion of the intestine) is removed. Appendectomy is normally performed as an urgent or emergency procedure to treat complicated acute appendicitis. Appendectomy may be performed laparoscopically (as minimally invasive surgery) or as an open operation. Over the 2010s, surgical practice has increasingly moved towards routinely offering laparoscopic appendicectomy; for example in the United Kingdom over 95% of adult appendicectomies are planned as laparoscopic procedures.
Genetic algorithmIn computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to generate high-quality solutions to optimization and search problems by relying on biologically inspired operators such as mutation, crossover and selection. Some examples of GA applications include optimizing decision trees for better performance, solving sudoku puzzles, hyperparameter optimization, causal inference, etc.
Genetic programmingIn artificial intelligence, genetic programming (GP) is a technique of evolving programs, starting from a population of unfit (usually random) programs, fit for a particular task by applying operations analogous to natural genetic processes to the population of programs. The operations are: selection of the fittest programs for reproduction (crossover), replication and/or mutation according to a predefined fitness measure, usually proficiency at the desired task.
Genetic genealogyGenetic genealogy is the use of genealogical DNA tests, i.e., DNA profiling and DNA testing, in combination with traditional genealogical methods, to infer genetic relationships between individuals. This application of genetics came to be used by family historians in the 21st century, as DNA tests became affordable. The tests have been promoted by amateur groups, such as surname study groups or regional genealogical groups, as well as research projects such as the Genographic Project. about 30 million people had been tested.
Triangular matrixIn mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called if all the entries above the main diagonal are zero. Similarly, a square matrix is called if all the entries below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero.
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Jordan normal formIn linear algebra, a Jordan normal form, also known as a Jordan canonical form (JCF), is an upper triangular matrix of a particular form called a Jordan matrix representing a linear operator on a finite-dimensional vector space with respect to some basis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately above the main diagonal (on the superdiagonal), and with identical diagonal entries to the left and below them. Let V be a vector space over a field K.
