Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I wonder if there is some agreed-upon best way to reconstruct the matrix of a positive definite operator A using "sampling" (like in tomography). More in detail I want to do this:

I have many small sets of basis functions. The sets are in general not orthogonal. I compute matrix elements <i|A|j>, where |i> and |j> belong to the same "set". In other words, in the non-orthogonal basis I know certain diagonal blocks of A, while the other elements are unknown. I want to determine an estimate of the off diagonal elements.

One way of reconstructing A is to simply take any orthogonal basis for the union of all basis functions, and then work with that. However, the orthogonal basis is not unique. My question is if there is a best way of doing this?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Reconstructing operator matrix from subspace samples

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**