Why Linear Algebra named in that way?
Especially, why we call it
linear? What does it mean?
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Linear algebra is so named because it studies linear functions. A linear function is one for which
$$f(x+y) = f(x) + f(y)$$
$$f(ax) = af(x)$$
where $x$ and $y$ are vectors and $a$ is a scalar. Roughly, this means that inputs are proportional to outputs and that the function is additive. We get the name 'linear' from the prototypical example of a linear function in one dimension: a straight line through the origin. However, linear functions can be more complex than this (or indeed, simpler: the function $f(x)=0$ for all $x$ is a linear function!
Of course, I've brushed a lot of detail under the carpet here. For example, what kind of space are $x$ and $y$ members of? (Answer: They're elements of a vector space). Do $x$ and $f(x)$ have to belong to the same space? (Answer: No). If they belong to different spaces, what does it mean to write $ax$ and $af(x)$? (Answer: you need an action by the same field on each of the vector spaces). Do the vector spaces have to be finite dimensional? (Answer: no, and in fact nearly all of the really interesting linear algebra takes place over infinite-dimensional vector spaces).
I hope that's enough to get you started.
From Moore in The axiomatization of linear algebra: 1875–1940 I've learned that:
The word "linear" means "of or pertaining to a line or lines". See http://jeff560.tripod.com/l.html for some of the earliest known uses of various types of "linear" objects.
The subject studies linear transformations between vector spaces. Hence the name. If you read up the definition of a linear transformation in Wikipedia, you will agree that the adjective linear is apt.