According to some guys who give advice on how to master different skills, i tried to decompose what it means for me "to know about linear algebra". I tried to be very specific, to make my goals measureable to stay motivated and assure i get into the right direction with my effors. The last 2 times i read books from A to Z.
I wasnt very pleased with the results, as i forgot about the concepts really fast and wasnt able to transfer the learned stuff to other fields, e.g. optmization, machine learning or circuit design.
So here is what i came up with what i think it means when i know about linear algebra:
1) Know the important definitions and be able to write them down, exact and from memory.
2) For every definition or abstract concept, be able to deliver an example for a useful application.
However, after 1 month of putting in 40 mins to 1 h a day constantly i struggle to answer questions were i need to make the transfer or application of the definitions/concepts by myself. For some concepts where the books dont provide an example of application, i struggle to figure one out by myself. If the context of the question or sometimes even the notation changes, i feel lost. Do you have an advice on what exact aspects of learning i should focus or what techniques i could use?