Suppose there are p-variate n observations represented by a matrix $X$ of dim $n$ x $p$.
$n$ : No of observations
$p$ : No of variables in each observation
So if i take the row-vector and draw all the observation in the p dimensional space then the observation point in given space shows that how each axis or dim (variable) is contributing(projection on that axis) for each observation(what i have understood by intuition).
What if i draw the column vector of $X$ in the n dim space? What does graphical representation is showing in that space? Why we need such type of representation? Does it mean for each vector(variable) how each observation(dimension) is contributing?