# What is the meaning of data represented as matrix in multivariate analysis?

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?

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.
• 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. – Creosote Oct 10 '15 at 14:03