Vtyjkyuk

Given that the bases of a vector and their duals satisfy:
$$epsilon^ie_j=delta^i_j$$
in which $epsilon$ and $e$ are the dual bases and bases respectively, and $delta^i_j$ is the Kronecker symbol, and that the definition of the dual vector space is:
$$V^*=varphi:V longrightarrow mathbbR$$
with $V$ being a vector space. Is it "correct" to think of the covector and vector as analogous to row and column vectors respectively ? I came to this conclusion due to the fact that the matrix product of a row vector and a column vector is a scalar, and $varphi$ also takes vectors to numbers, but I have a feeling that I'm still missing something.

Thanks in advance!

P/s: I also find this way of thinking of vectors and covectors very nice since row and column vectors are sort of doppelgängers, hence the covectors and dual spaces

It is partially correct, or at least meaningful. Indeed, given $v in V$ and $w in V^*$, if you choose dual bases, you have that $w(v)=w^Tv$ (check this). But note that I am considering all vectors as vertical and then transposing $w$, since in principle $V^*$ is not a special vector space, so that it is not very precise to write its vectors in a different way.