For me I think the difficulty was just reconciling reality with the concept of a coordinate system. I think it was just some abstract concept that I considered to be out of my cognitive reach of understanding. I just had no way to anchor anything being said to me to a concept I had in my head at the time.
I remember this poor teaching fellow where I went to Lehigh University where I studied Mechanical Engineering. He was foreign and had the honor of teaching us Linear Algebra. He must have noticed that none of us had even the slightest damn clue what he was talking about. So, the class before every exam, he would literally just give go over the exam problems nearly verbatim and solve them. I came out of that class with a good grade and not the slightest fucking understanding of Linear Algebra beyond the very superficial algebraic laws of multiplying tensor objects (i.e., scalars (0-D tensor), vectors (1-D tensor), and matrices).
I'd like to thank Grant Sanderson (3Blue1Brown) and Mike Cohen (Udemy Linear Algebra course using Matlab and Python) for teaching me linear algebra. And don't forget Gilbert Strang, of course!! (find his course on MIT OCW) The visualizations of the tensors transforming provided by the first two are what really made Linear Algebra start to click for me. I want to go back to Gilbert Strang's course now that I have a better geometric understanding of what is happening and appreciate all his wisdom on the subject.
As a physics major at the time, I think that learning physics in addition to multivar and linear algebra is so handy in terms of providing reference material for intuitions.
Also, learning it as part of a numerical computing stack (like python) where you can experiment and visualize is huge for building intuition.
I remember this poor teaching fellow where I went to Lehigh University where I studied Mechanical Engineering. He was foreign and had the honor of teaching us Linear Algebra. He must have noticed that none of us had even the slightest damn clue what he was talking about. So, the class before every exam, he would literally just give go over the exam problems nearly verbatim and solve them. I came out of that class with a good grade and not the slightest fucking understanding of Linear Algebra beyond the very superficial algebraic laws of multiplying tensor objects (i.e., scalars (0-D tensor), vectors (1-D tensor), and matrices).
I'd like to thank Grant Sanderson (3Blue1Brown) and Mike Cohen (Udemy Linear Algebra course using Matlab and Python) for teaching me linear algebra. And don't forget Gilbert Strang, of course!! (find his course on MIT OCW) The visualizations of the tensors transforming provided by the first two are what really made Linear Algebra start to click for me. I want to go back to Gilbert Strang's course now that I have a better geometric understanding of what is happening and appreciate all his wisdom on the subject.