linear map

(redirected from Bijective linear map)

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 ?
Let T: C(X) [right arrow] C(Y) be a continuous bijective linear map such that Te never vanishes.
Since dim(V [and] V) = 3 = dimV, both [eta] and [pi] are bijective linear maps. Now the linear endomorphism [eta][[pi].sup.-1] : V [right arrow] V is definite, because otherwise there would exist an element u [member of] V \ {0} such that ([eta][[pi].sup.-1](u), u) = 0.