All Questions

I was thinking if it is possible to define an inner product between two small physical objects with a positive definite kernel and was led to look at the Rydberg formula: The Rydberg formula for ...

I will word this question in terms of linear operators acting on $\mathbb{C}^n$ for simplicity. Feel free to provide an answer in terms of more general Hilbert spaces if you think it makes more sense ...

Let $x_0, x_1, \ldots x_{n-1}$ be arbitrary vectors in a complex Hilbert space. Define the $n \times n$ symmetric real matrix $M$ by $M_{ij} = \lvert \langle x_i, x_j \rangle \rvert^2$. Must $M$ be ...