This is the problem I had with Linear Algebra. The first half of the class felt like I was just being drilled definitions. But once all the definitions click, it's rather simple.
The best thing about my linear algebra class was that the professor warned us about this up front. Yet, I still was not prepared for the onslaught of new words, and the bad part of the class is they were all defined in terms of more mathematical words, not concepts like this rubber band example.
That was the point of the "What are eigen values?" article. It was to give the intuition behind the scary mathematical definition.
I find this helpful, as it answers the all important questions 1) Why should I care? and 2) What is the basic problem that the scary math is trying to solve?
With answers to those questions in hand, you can return to the scary math and work out how it maps to those answers.
Is there something specific about the parent post that you don't understand that I can try to explain?