Linear algebra is a shared field across multiple disciplines. So I'm sure that there are many valid and useful interpretations as to what "linear algebra" is essentially about.
However, in mathematics proper, it is absolutely the case that linear algebra is about linear transformations. Indeed, this is the only interpretation that remains meaningful when trying to generalize (e.g. to functional analysis / multilinear algebra).
However, in mathematics proper, it is absolutely the case that linear algebra is about linear transformations. Indeed, this is the only interpretation that remains meaningful when trying to generalize (e.g. to functional analysis / multilinear algebra).