Vector spaceIn mathematics and physics, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field. The operations of vector addition and scalar multiplication must satisfy certain requirements, called vector axioms. The terms real vector space and complex vector space are often used to specify the nature of the scalars: real coordinate space or complex coordinate space.
Associative algebraIn mathematics, an associative algebra A is an algebraic structure with compatible operations of addition, multiplication (assumed to be associative), and a scalar multiplication by elements in some field K. The addition and multiplication operations together give A the structure of a ring; the addition and scalar multiplication operations together give A the structure of a vector space over K. In this article we will also use the term [[algebra over a field|K-algebra]] to mean an associative algebra over the field K.
Non-associative algebraA non-associative algebra (or distributive algebra) is an algebra over a field where the binary multiplication operation is not assumed to be associative. That is, an algebraic structure A is a non-associative algebra over a field K if it is a vector space over K and is equipped with a K-bilinear binary multiplication operation A × A → A which may or may not be associative. Examples include Lie algebras, Jordan algebras, the octonions, and three-dimensional Euclidean space equipped with the cross product operation.
Euclidean spaceEuclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes.
Place des ArtsPlace des Arts is a major performing arts centre in Montreal, Quebec, Canada, and the largest cultural and artistic complex in Canada. Home to the Montreal Symphony Orchestra, the Orchestre Métropolitain, Les Grands Ballets Canadiens, and the Opéra de Montréal, the complex is situated between Saint Catherine and de Maisonneuve Streets, and Saint-Urbain and Jeanne-Mance streets, in an area now known as the Quartier des spectacles in the borough of Ville-Marie.
Graded vector spaceIn mathematics, a graded vector space is a vector space that has the extra structure of a grading or gradation, which is a decomposition of the vector space into a direct sum of vector subspaces, generally indexed by the integers. For "pure" vector spaces, the concept has been introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures. Let be the set of non-negative integers.
QuebecQuebec (k(w)ɪˈbɛk ; kwəˈbɛk ; Québec kebɛk) is one of the thirteen provinces and territories of Canada. It is the largest province by area and the second-largest by population. Much of the population of Quebec lives in urban areas along the St. Lawrence River, between its most populous city, Montreal, and the provincial capital, Quebec City. The province is the home of the Québécois nation.
RéunionRéunion, officially Department of Réunion, is an island in the Indian Ocean that is an overseas department and region of France. Part of the Mascarene Islands, it is located approximately east of the island of Madagascar and southwest of the island of Mauritius. , it had a population of 873,102. Its capital and largest city is Saint-Denis. Réunion was uninhabited until French immigrants and colonial subjects settled the island in the 17th century.
Common lawIn law, common law (also known as judicial precedent, judge-made law, or case law) is the body of law created by judges and similar quasi-judicial tribunals by virtue of being stated in written opinions. The defining characteristic of common law is that it arises as precedent. Common law courts look to the past decisions of courts to synthesize the legal principles of past cases. Stare decisis, the principle that cases should be decided according to consistent principled rules so that similar facts will yield similar results, lies at the heart of all common law systems.
Banach spaceIn mathematics, more specifically in functional analysis, a Banach space (pronounced ˈbanax) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vectors and is complete in the sense that a Cauchy sequence of vectors always converges to a well-defined limit that is within the space. Banach spaces are named after the Polish mathematician Stefan Banach, who introduced this concept and studied it systematically in 1920–1922 along with Hans Hahn and Eduard Helly.
Common carrierA common carrier in common law countries (corresponding to a public carrier in some civil law systems, usually called simply a carrier) is a person or company that transports goods or people for any person or company and is responsible for any possible loss of the goods during transport. A common carrier offers its services to the general public under license or authority provided by a regulatory body, which has usually been granted "ministerial authority" by the legislation that created it.
Common Agricultural PolicyThe Common Agricultural Policy (CAP) is the agricultural policy of the European Union. It implements a system of agricultural subsidies and other programmes. It was introduced in 1962 and has since then undergone several changes to reduce the EEC budget cost (from 73% in 1985, to 37% in 2017) and consider rural development in its aims. It has however, been criticised on the grounds of its cost, its environmental, and humanitarian effects.
Emmanuel MacronEmmanuel Jean-Michel Frédéric Macron (emanɥɛl makʁɔ̃; born 21 December 1977) is a French politician serving as President of France since 2017. Ex officio, he is also one of the two Co-Princes of Andorra. Earlier, he served as the Minister of Economics, Industry and Digital Affairs under President François Hollande from 2014 to 2016 and Deputy Secretary-General to the President from 2012 to 2014. Born in Amiens, Macron studied philosophy at Paris Nanterre University, later completing a master's degree in public affairs at Sciences Po and graduating from the École nationale d'administration in 2004.
