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Tensor Representations
In mathematics, the tensor representations of the general linear group are those that are obtained by taking finitely many tensor products of the fundamental representation and its dual. The irreducible factors of such a representation are also called tensor representations, and can be obtained by applying Schur functors (associated to Young tableaux). These coincide with the rational representations of the general linear group. More generally, a matrix group is any subgroup of the general linear group. A tensor representation of a matrix group is any representation that is contained in a tensor representation of the general linear group. For example, the orthogonal group O(''n'') admits a tensor representation on the space of all trace-free symmetric tensors of order two. For orthogonal groups, the tensor representations are contrasted with the spin representations. The classical groups, like the symplectic group In mathematics, the name symplectic group can refer to two di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
