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Dimension (vector space) 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 .
Vapnik–Chervonenkis dimension. In Vapnik–Chervonenkis theory, the Vapnik–Chervonenkis (VC) dimension is a measure of the size (capacity, complexity, expressive power, richness, or flexibility) of a class of sets. The notion can be extended to classes of binary functions. It is defined as the cardinality of the largest set of points that ...
Dimension theorem for vector spaces. In mathematics, the dimension theorem for vector spaces states that all bases of a vector space have equally many elements. This number of elements may be finite or infinite (in the latter case, it is a cardinal number ), and defines the dimension of the vector space. Formally, the dimension theorem for ...
In mathematics. In mathematics, the dimension of an object is, roughly speaking, the number of degrees of freedom of a point that moves on this object. In other words, the dimension is the number of independent parameters or coordinates that are needed for defining the position of a point that is constrained to be on the object.
The zero vector is given by the constant function sending everything to the zero vector in V. The space of all functions from X to V is commonly denoted V X. If X is finite and V is finite-dimensional then V X has dimension |X|(dim V), otherwise the space is infinite-dimensional (uncountably so if X is infinite).
Codimension. In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties . For affine and projective algebraic varieties, the codimension equals the height of the defining ideal. For this reason, the height of an ideal is often called ...
The dimension of V is. The maximal length of the chains of distinct nonempty (irreducible) subvarieties of V. This definition generalizes a property of the dimension of a Euclidean space or a vector space. It is thus probably the definition that gives the easiest intuitive description of the notion.
Software development. The V-model is a graphical representation of a systems development lifecycle. It is used to produce rigorous development lifecycle models and project management models. The V-model falls into three broad categories, the German V-Modell, a general testing model, and the US government standard. [ 2]