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In control engineering and system identification, a state-space representation is a mathematical model of a physical system specified as a set of input, output, and variables related by first-order differential equations or difference equations.
State spaces are useful in computer science as a simple model of machines. Formally, a state space can be defined as a tuple [N, A, S, G] where: . N is a set of states; A is a set of arcs connecting the states
Vector space model or term vector model is an algebraic model for representing text documents (or more generally, items) as vectors such that the distance between vectors represents the relevance between the documents.
Here, the motivating example is the C*-algebra (), where X is a locally compact Hausdorff topological space. By definition, this is the algebra of continuous complex-valued functions on X that vanish at infinity (which loosely means that the farther you go from a chosen point, the closer the function gets to zero) with the operations of ...
The parameter space is the space of all possible parameter values that define a particular mathematical model. It is also sometimes called weight space, and is often a subset of finite-dimensional Euclidean space. In statistics, parameter spaces are particularly useful for describing parametric families of probability distributions.
Discretization is also concerned with the transformation of continuous differential equations into discrete difference equations, suitable for numerical computing.. The following continuous-time state space model
A latent space, also known as a latent feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another. Position within the latent space can be viewed as being defined by a set of latent variables that emerge from the resemblances from the objects.
A space M is a coarse moduli space for the functor F if there exists a natural transformation τ : F → Hom(−, M) and τ is universal among such natural transformations. More concretely, M is a coarse moduli space for F if any family T over a base B gives rise to a map φ T : B → M and any two objects V and W (regarded as families over a ...