Basic issue but one that created a moment of reflection for me. In studying PCA we use the unit vector $\vec{w}_{1}$ and reproject all observations $\vec{x}_{n}$ onto this via the formula:
$\vec{w}_{1}^{T} \cdot \vec{x}_n{}$
Normally the result of the product between these two elements should be a scalar but from the page where this example was taken it would appear to be a vector. I'm probably missing something.
