Bessel's inequality
Let $(e_k)$ be an orthonormal sequence in an inner product space X. Then, for every $x\in X $
$\sum_{k=1}^{n}|\langle x,e_k\rangle|^2 \leq||x||^2$
I want to interpret Bessel's inequality geometrically when $ X=R^r$ and $r\geq n$
When looking at $R^2$, the LHS behaves as the sum of squares of the side lengths of a triangle and RHS as the third side of the triangle.
But I don't know whether this is correct, and I would like to know how we interpret this in higher dimensions.