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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 ...
Representational space (lived space): The individual, subjective experience of space, shaped by symbols, images, and personal emotions. Physical space is constructed by various actors, e.g. the state, landowners and architects. Discursive space is mentally constructed by the way the space is discussed and represented.
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.
First Space is the empirical construction of space. Empirical space refers to the process whereby the mundane fabric of daily life is constructed. These simple things like, cars, houses, mobiles, computers, and roads are very simple but they are great achievements of our daily life and they play very important role in making up who we are today.
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The real part of is a continuous real linear functional on and so the Riesz representation theorem may be applied to := and the associated real Hilbert space (, ,, ) to produce its Riesz representation, which will be denoted by .
A typical approach for choosing a particular type of scale space representation is to establish a set of scale-space axioms, describing basic properties of the desired scale-space representation and often chosen so as to make the representation useful in practical applications. Once established, the axioms narrow the possible scale-space ...
Group representation, describes abstract groups in terms of linear transformations of vector spaces; Representation of a Lie group, a linear action of a Lie group on a vector space; Lie algebra representation, a way of writing a Lie algebra as a set of matrices in such a way that the Lie bracket is given by the commutator