I am currently struggling to get my head around what eigenvalues and eigenvectors truly are as Khan Academy says that eigenvalues are just a scalar by which a vector is scaled and the eigenvector is the resultant vector that is not equal to zero, but other sources say different things.

I was wondering whether someone would be able to provide a simple explanation of what eigenvalues and eigenvectors are, and it would be greatly appreciated if a visual supplement is provided. I need to learn these to find the general solution to a markov matrix and am becoming quite confused.

Thanks!