Linear transforms of vector spaces has the linearity (i.e., homogeneity and superimposability), which is shared by LTI system. There are also shared concepts such as eigenvectors/eigenvalue...
I am wondering, can linear transforms (of vector spaces) be seen as LTI systems? If not, why? If yes, in particular, are there counterparts in vector spaces for the concept of Dirac $\delta$ and $h(t)$ in LTI systems, where $\delta$ represents all possible inputs (e.g., from frequency space point of view), and thus $h(t)$ characterizes the LTI system? If these two counterparts exists in Linear transforms, what's the counterpart for convolution?
A little background: I had this question recently as I am studying linear algebra (starting from some basics) ...actually I first read some books on DSP/DIP a couple months ago, and then I find out that I need to learn some basics of linear algebra (as well as other branches of math), otherwise most of the DSP/DIP literature are foreign to me...in other words, I am also new to the field of DSP/DIP...so I beg your pardon that my question may be a bit fuzzy.