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A diagram of dimensions 1, 2, 3, and 4. In mathematics, the dimension of a vector space V is the cardinality (i.e., the number of vectors) of a basis of V over its base field. [1] [2] It is sometimes called Hamel dimension (after Georg Hamel) or algebraic dimension to distinguish it from other types of dimension.
In quantum field theory, there exist quantum categories. [16] [17] [18] and quantum double groupoids. [18]One can consider quantum double groupoids to be fundamental groupoids defined via a 2-functor, which allows one to think about the physically interesting case of quantum fundamental groupoids (QFGs) in terms of the bicategory Span(Groupoids), and then constructing 2-Hilbert spaces and 2 ...
Divine Proportions does not assume much in the way of mathematical background in its readers, but its many long formulas, frequent consideration of finite fields, and (after part I) emphasis on mathematical rigour are likely to be obstacles to a popular mathematics audience. Instead, it is mainly written for mathematics teachers and researchers.
In mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety (and by extension that of a scheme).The need of a theory for such an apparently simple notion results from the existence of many definitions of dimension that are equivalent only in the most regular cases (see Dimension of an algebraic variety).
Desargues's theorem is true for any projective space of dimension at least 3, and more generally for any projective space that can be embedded in a space of dimension at least 3. Desargues's theorem can be stated as follows: If lines Aa, Bb and Cc are concurrent (meet at a point), then the points AB ∩ ab, AC ∩ ac and BC ∩ bc are collinear.
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For example, the dimension of a point is zero; the dimension of a line is one, as a point can move on a line in only one direction (or its opposite); the dimension of a plane is two etc. The dimension is an intrinsic property of an object, in the sense that it is independent of the dimension of the space in which the object is or can be embedded.
Created Date: 8/30/2012 4:52:52 PM