Suppose that we have a portfolio of $n$ assets.

A perfectly diversified portfolio is one in which each asset has equal weights, i.e. each asset has weight $\frac{1}{n}$. Of course this is usually not the case.

What are some of the ways we can measure how well diversified our portfolio is?

We could measure how far our portfolio is from the equally-weighted portfolio.

This of course will depend on the geometry of the space which is not euclidean since the sum of the weights must be one.