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The social production of space is a concept in the sociology of space which contends that space is neither a thing nor a container, but a product and means of production. Thus, space is produced and constructed socially and a set of human relations. [1] It was pioneered by philosopher Henri Lefebvre in his 1974 book La Production de l'espace. [2]
Representation of space (conceived space): i.e., conceptualized representations of space; space as developed cognitively. "[C]onceptualized space, the space of scientists, planners ... [t]his is the dominant space in any society (or mode of production)." [15] Representational spaces (lived space): i.e
Trouvelot, The great nebula in Orion (1875).. Astronomical art is a genre of space art that focuses on visual representations of outer space.It encompasses various themes, including the space environment as a new frontier for humanity, depictions of alien worlds, representations of extreme phenomena like black holes, and artistic concepts inspired by astronomy.
The term representation of a group is also used in a more general sense to mean any "description" of a group as a group of transformations of some mathematical object. More formally, a "representation" means a homomorphism from the group to the automorphism group of an object. If the object is a vector space we have a linear representation.
The vector cross product, used to define the axis–angle representation, does confer an orientation ("handedness") to space: in a three-dimensional vector space, the three vectors in the equation a × b = c will always form a right-handed set (or a left-handed set, depending on how the cross product is defined), thus fixing an orientation in ...
For example, when rotating a stationary (zero momentum) spin-5 particle about its center, is a rotation in 3D space (an element of ()), while () is an operator whose domain and range are each the space of possible quantum states of this particle, in this example the projective space associated with an 11-dimensional complex Hilbert space .
The vector space V is called the representation space of φ and its dimension (if finite) is called the dimension of the representation (sometimes degree, as in [18]). It is also common practice to refer to V itself as the representation when the homomorphism φ is clear from the context; otherwise the notation ( V , φ ) can be used to denote ...
The representation space of this subrepresentation is then finite-dimensional. The degree of a representation is the dimension of its representation space . The notation is sometimes used to denote the degree of a representation .