# linear map

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Related to linear map: linear operator

## linear map

(mathematics)
(Or "linear transformation") A function from a vector space to a vector space which respects the additive and multiplicative structures of the two: that is, for any two vectors, u, v, in the source vector space and any scalar, k, in the field over which it is a vector space, a linear map f satisfies f(u+kv) = f(u) + kf(v).
References in periodicals archive ?
In order to prove the following Theorem 3.2, which characterizes the form of the linear map preserving the left spectrum of 2 x 2 quaternion matrices, we need the following lemmas.
From  (Example 2.13) we know that if one considers the linear map [alpha]: A [right arrow] A given by
* For an arbitrary vector space W, we denote by Hom(W, C) the set of all linear maps from W to C.
A bilinear map is a function [phi] : U [right arrow] D such that for any a [member of] A the map b [??] [phi](a, b) is linear map from B to D, and for any b [member of] B the map a [??] [phi](a, b) is linear map from A to D.
This minimization problem is always uniquely solvable, and as the optimal linear map minimizing (3.2) we obtain
We shall now show that each [PHI] [member of] M defines a continuous linear map from B into B.
Understanding the correspondence between matrices and affine transformations can help to clarify the meaning of such key notions from Linear algebra and Geometry such as the linear map, affine map, image and kernel of an affine map, composition of affine maps and transformation of the coordinate system.
A linear map T: C(X) [right arrow] C(Y) is called Separating (, p.2) if fg [equivalent to] 0 implies TfTg [equivalent to] 0.
The output graph is a piecewise linear map, which is possibly make as a smooth curve by standard methods or by new one.
If you are someone who prefers a maze instead of a linear map, this will be your thing.
Let S be a subset of a vector space over [Z.sub.2] and choose a random linear map to a smaller vector space R.
Recall from Part I that we defined for any abelian F-variety A a number [rank.sub.[Delta]](A) called its [Delta]-rank; it is simply the rank of the linear map

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