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A map is a function, as in the association of any of the four colored shapes in X to its color in Y. In mathematics, a map or mapping is a function in its general sense. [1] These terms may have originated as from the process of making a geographical map: mapping the Earth surface to a sheet of paper. [2]
A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, for any nonnegative integer , a multilinear map of k variables is called a k-linear map. If the codomain of a multilinear map is the field of scalars, it is called a multilinear form.
In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication.
Depending on the value of μ, the tent map demonstrates a range of dynamical behaviour ranging from predictable to chaotic. If μ is less than 1 the point x = 0 is an attractive fixed point of the system for all initial values of x i.e. the system will converge towards x = 0 from any initial value of x.
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Maps may be parameterized by a discrete-time or a continuous-time parameter.
A linear map : is called a positive map if maps positive elements to positive elements: (). Any linear map ϕ : A → B {\displaystyle \phi :A\to B} induces another map id ⊗ ϕ : C k × k ⊗ A → C k × k ⊗ B {\displaystyle {\textrm {id}}\otimes \phi :\mathbb {C} ^{k\times k}\otimes A\to \mathbb {C} ^{k\times k}\otimes B}
At the same time, the mapping of a function to the value of the function at a point is a functional; here, is a parameter. Provided that f {\displaystyle f} is a linear function from a vector space to the underlying scalar field, the above linear maps are dual to each other, and in functional analysis both are called linear functionals .
xy plot where x = x 0 ∈ [0, 1] is rational and y = x n for all n. The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map [1] [2]) is the mapping (i.e., recurrence relation)
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