Sentence examples for as a linear map from inspiring English sources
The magnetic map is expressed as a linear map.
We define F i s : G → G Open image in new window by v ↦ Ad(exp(s v i )v) as a linear map, for i = 1,2,3.
As a linear map, it can be described by a matrix, once a basis is introduced on H p ( G ). Remark We can focus on graph automorphisms because the image im ( T ) is T-invariant and T restricted to the attractor im ( T n ) for sufficiently large n is an automorphism.
Given that (k[Vtimes V]) is canonically isomorphic to (k[V]otimes k[V]), this is the same as a linear map begin{aligned} k[V]otimes k[V]rightarrow V. end{aligned}A formal multiplication (F) is a formal loop if begin{aligned} F|_{1otimes k[V]}=pi _V=F|_{k[V]otimes 1}, end{aligned}where (pi _V k[V]rightarrow V) is the projection of a polynomial onto its linear part.
The operator ℋ is then seen as a linear mapping from the reflectivity variable s to the scattering operator ℋ(s).
An exponential mapping from payoff to fitness has exactly the same properties as a linear mapping in most cases, but it allows greater variation in the intensity of selection and is thus more general.
Equations (1)–(3) can be summarised as a linear mapping Λ from the incoming to outgoing fluxes where 𝓖 represents the Green's operator that solves Eq. (1) with boundary condition [ Eq. (2)] and 𝓜 is the measurement operator that restricts Φ to the detector surface Γ2.
Since E u = 0 in Ω j and L - u = 0 on Σ j, u = a j + B j x on each connected component Ω j, j = 1,..., m, and u = 0 in ℝ n Ω ¯ 0. Note that this is true also for n = 2, because φ ∈ W - implies ∫ Σ φ d σ = 0. We can define a linear map τ as follows τ : W - → ( ℝ n × S n ) m φ → ( a 1, B 1, …, a m, B m ).
An important example is the kernel of a linear map for some fixed matrix A, as above.
For an element x ∈ V, let L ( x ) be a linear map of V defined as L ( x ) y = x ∘ y.
