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5 $begingroup$ I am currently self studying Linear Algebra Done Right . I am doing OK and currently on Chapter 3 Linear Maps. My understanding now is that a map is like a function that maps something to another thing. Why people like to particularly define linear maps? Just curious..maybe there are non-linear maps? Another stupid question is that is linear maps really look like a straight line in some specific examples, like, $u, v $ is 1 dimensional vector space. And then $T(u+v) = T(u) + T(v)$ Or put it in another way why it is called linear map. And finally, why linear maps have the additivity and homogeneity properties? linear-algebra share | cite | improve this question