[matteuan]

The only way to test is if you talk with an expert and he says you have understood. There are many things in linear algebra that you can use in practice even when you didn't really understand them. This is the reason why self-studying certain topics is very hard, you still need (good) teachers to give you constant feedback.

[ukj]

That seems like a verbalistic notion of 'understanding'.

How do I falsify the expert's claims about my understanding?