Original Post

If we have two states in vector representation on infinitely-dimensional Hilbert space, and we're trying to trace the transition probabilities from one such state to another, this is what all this operator theory is about. Collecting tons of cross-correlation or mutual information data in your design matrices seem to help building statistical models that can be represented as Hermitian operators acting on the vectors in Hilbert space. When #eigenvalues are mentioned in all kinds of contexts, these apply to these transformational operators, and study the operators' inner structure. Why so little literature mentions how all these fundamental concepts relate and how we apply them, at the places where we use them?

#matrices #tensors #operators #controltheory #quantumphysics #generalrelativity