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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?

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The $c^\textrm{th}$ column vector is just all the $c^\textrm{th}$-component values. For example, with $p=3$ and vectors consisting of (age,height,weight), the $2^\textrm{nd}$ column is just all of the heights in your data.

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  • $\begingroup$ What is mean by plotting each of the column vector in the n dim space. What that vector is representing? $\endgroup$ – Sanjeev Oct 10 '15 at 13:47
  • $\begingroup$ That vector is just a single point in $n$ dimensional space. It represents nothing more than what I described previously. It's not a particularly useful way of looking at the data. $\endgroup$ – Creosote Oct 10 '15 at 14:03
  • $\begingroup$ It is clear that a single height vector represents all the heights. I would like to know what aspect of data we are analysing when we are representing the bunch of row vectors of the matrix with axis representing the age, heigh and weight w.r.t the column vector in the space with axis representing each observation. $\endgroup$ – Sanjeev Oct 10 '15 at 14:22

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