Is there a term for the fact that research is done only with the means available?

In my university, people often call limitations as 'constraints'.

I have heard them saying:

"resource constraints" - availability of computers and machines, people

"financial constraints" - Money

"space constraints" - Physical space (room), lab etc.

"practical limitations" could cover just about any type of situation where you don't have the means to do what you'd ideally like to do.

"resource limitations" could cover not having enough time, money, or trained people to do the work, not having the right equipment, and a lot of other things.

"equipment limitations" could cover not having enough equipment, or the equipment you have can't do what you need.

I would lean towards words like tractability/intractability to describe problems. A problem that is intractable can, in theory, be done but, in practice, is not possible. For instance, you mention inversion of a matrix - in theory, the steps and processes required to invert a matrix of any size are clearly defined - it just is a matter of resources and time. However, in practice, the amount of resources and time required are unacceptably large.

Wikipedia has this to say about the matter:

A problem that can be solved in theory (e.g. given large but finite resources, especially time), but for which in practice any solution takes too many resources to be useful, is known as an intractable problem.[13] Conversely, a problem that can be solved in practice is called a tractable problem, literally "a problem that can be handled". The term infeasible (literally "cannot be done") is sometimes used interchangeably with intractable,[14] though this risks confusion with a feasible solution in mathematical optimization.[15]

which seems to reasonably approach what you are trying to express.