Reviewing notes 1.1 of Advanced algebra
♦Linear map
Definition
Linear map
A linear map from vector space V to W over a field F is a function T with the following properties:
Additivity:
T(u+v)=T(u)+T(v) for every u,v∈V.
Homogeneity:
T(λv)=λT(v) for v∈V and λ∈F.
Example
Linear map zero
In addition to its other uses,we let the symbol 0 denote the function that takes each element of some vector space to the additivei dentity of another vector space. Usually, the context should allow you to distinguish between the many uses of the symbol 0.
Identity
The identity map, denoted I, is the functionon of some vector space that takes each element to itself.
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