In mathematics, the classical groups are defined as the special linear groups over the reals R {\displaystyle \mathbb {R} } , the complex numbers C {\displaystyle...

In Weyl's wonderful and terrible1 book The Classical Groups [W] one may discern two main themes: first, the study of the polynomial invariants for an arbitrary...

Artin investigated the orders of such groups, with a view to classifying cases of coincidence. A classical group is, roughly speaking, a special linear...

U(n), consisting of all n×n unitary matrices. As a compact classical group, U(n) is the group that preserves the standard inner product on C n {\displaystyle...

local fields, finite fields, and adele rings. The symplectic group is a classical group defined as the set of linear transformations of a 2n-dimensional...

foundational component of Western culture, classical music is frequently seen from the perspective of individual or groups of composers, whose compositions, personalities...

isomorphic to the group of n {\displaystyle n} th roots of unity in the field F {\displaystyle F} . The so-called classical groups are subgroups of GL...

mathematics, the finite-dimensional representations of the complex classical Lie groups G L ( n , C ) {\displaystyle GL(n,\mathbb {C} )} , S L ( n , C )...

symplectic groups but it is possible to construct more using division algebras (for example the unit group of a quaternion algebra is a classical group). Note...

homogeneous space for the corresponding classical group. When k is strictly less than n then the special orthogonal group SO(n) also acts transitively on V...

} ⁠. These are now called the classical groups, as the concept has been extended far beyond these origins. Lie groups are named after Norwegian mathematician...

Classical liberalism is a political tradition and a branch of liberalism that advocates free market and laissez-faire economics and civil liberties under...

^{3}} , which is equivalent to requiring them to preserve length. See classical group for a treatment of this more general approach, where SO(3) appears...

The classical Lie algebras are finite-dimensional Lie algebras over a field which can be classified into four types A n {\displaystyle A_{n}} , B n {\displaystyle...

Classics, also classical studies or Ancient Greek and Roman studies, is the study of classical antiquity. In the Western world, classics traditionally...

Classical Greece was a period of around 200 years (the 5th and 4th centuries BC) in ancient Greece, marked by much of the eastern Aegean and northern...

The Classical period was an era of classical music between roughly 1750 and 1820. The classical period falls between the Baroque and Romantic periods...

Indian classical dance, or Shastriya Nritya, is an umbrella term for different regionally-specific Indian classical dance traditions, rooted in predominantly...

of view of Lie theory, the classical unitary group is a real form of the Steinberg group 2An, which is an algebraic group that arises from the combination...

of the classical groups and the groups of exceptional type in a 1955 paper. This omitted certain known groups (the projective unitary groups), which...

Poincaré group, with rotations being produced as the composition of an even number of reflections. In classical physics, the Galilean group is a comparable...

reflection group. In fact it turns out that most finite reflection groups are Weyl groups. Abstractly, Weyl groups are finite Coxeter groups, and are important...

of classical groups, and other related groups. One such family of groups is the family of general linear groups over finite fields. Finite groups often...

rock band or the Baroque chamber group for basso continuo (harpsichord and cello) and one or more singers. In classical music, trios or quartets either...

Classical Latin is the form of Literary Latin recognized as a literary standard by writers of the late Roman Republic and early Roman Empire. It formed...

space R {\displaystyle \mathbb {R} } n×n. Another classical group is the orthogonal group O(n), the group of all linear maps from R {\displaystyle \mathbb...

Neoclassical architecture, sometimes referred to as Classical Revival architecture, is an architectural style produced by the Neoclassical movement that...

A classical planet is an astronomical object that is visible to the naked eye and moves across the sky and its backdrop of fixed stars (the common stars...

Masterworks Records. The CBS Records Group was acquired by Sony in 1988, and in 1990 it was renamed Sony Classical. Sony Classical has represented artists including:...

Classical mechanics is a physical theory describing the motion of objects such as projectiles, parts of machinery, spacecraft, planets, stars, and galaxies...