  In \cite{GQ2008} R. Gow and R. Quinlan have cast a new look on the
endomorphism algebra of a $K$-vector space $V$ of dimension $n$ assuming that
$K$ has a Galois extension $L$ of degree $n$. In this approach the $K$-space
$L$ may serve as a model for $V$ and Galois-theoretic ideas and results may be
applied to elucidate the structure of endomorphisms and other important objects
of linear algebra. In particular, this leads to the clarification of the
structure of a rank-one endomorphism, trace of an endomorphism, criteria for
linear indepedence etc. We present an exposition of these results using the
language of tensor algebra wherever possible to provide shorter and more
conceptual proofs.
