I took LinAlg the same semester I took Computer Graphics, back in 2001. The first half of LinAlg was all about solving equations, transformation matrices and that sort of stuff, and the first half CG was all 2D drawing (Bresenham and such). Second half of CG was all about OpenGL, and I was able to apply all the stuff I'd just learned in LinAlg.
The second half of LinAlg was a bunch of stuff about Eigenthis and Eigenthat, with no particular explanation as to what you'd use it for or why you would care. I pass the class with an A and was even recommended by the instructor to be work as a tutor for other students, but 23 years later I couldn't tell you the use of any of that stuff.
T-matrices, though - I've used that stuff my whole career, working in medical imaging and related fields. I still couldn't tell you what an Eigenvalue or Eigenvector is useful for, as I never had any reason to apply that stuff.
It's not particularly abstract if you can explain why and how this stuff is used - and I know it's heavily used in many fields - just not those that I've worked in.
Eigenvectors characterise a linear transformation by answering a simple question: What lines map to themselves after the transformation?
Say for example you rotate something in 3D. The rotation axis remains unchanged. That's an eigenvector. Or say you mirror something in 3D, then all the lines lying in the mirror plane remain unchanged (all eigenvectors with eigenvalue 1), and the line orthogonal to the mirror plane remains unchanged - or rather, flipped, so it's an eigenvector with eigenvalue -1.
Yeah, eigenvectors and eigenvalues are abstract and best understood in terms of the linear mapping between vector spaces and change of basis, but change of basis for a vector space and writing a matrix in a new basis gets really complicated. Many people get lost there.
The second half of LinAlg was a bunch of stuff about Eigenthis and Eigenthat, with no particular explanation as to what you'd use it for or why you would care. I pass the class with an A and was even recommended by the instructor to be work as a tutor for other students, but 23 years later I couldn't tell you the use of any of that stuff.
T-matrices, though - I've used that stuff my whole career, working in medical imaging and related fields. I still couldn't tell you what an Eigenvalue or Eigenvector is useful for, as I never had any reason to apply that stuff.
It's not particularly abstract if you can explain why and how this stuff is used - and I know it's heavily used in many fields - just not those that I've worked in.