ABSTRACT
Manipulating matrices is not what linear algebra is all about. The matrices are only a convenient tool to represent and keep track of linear maps. And that too when the domain (and hence the range also) of such a function is finite dimensional. In its full generality, linear algebra is the study of functions in the most general context, which behave like the real valued function
f(x) = mx (1.1)
of real variable x. The graph of (1.1) is a straight line through the origin with fixed slope m. Hence the name linear algebra.
