At least from a non-software engineering context, you're usually taught eigenvalues first as they are quite useful for a lot different problems... basically all

At least from a non-software engineering context, you're usually taught eigenvalues first as they are quite useful for a lot different problems... basically all linear systems. At least the way our curriculum was arranged, in first year had a 'simple' linear algebra course that consisted of solving systems of linear equations (like Gaussian Elimination), and 'simple' things with matrices and vectors, which then ended in this rush to teach eigen-decomposition, which we pretty much just learned by rote. I don't believe anyone really had a feel for what we were actually doing. But the flip side was that we learned eigen-decomposition in time for all the 'fun' applications of it, and by the time our far more rigorous linear algebra course occurred in 3rd year (which ended with SVD), when we went over eigen-decomp again, it was like a brilliant 'OH, I GET ITT' moment for everyone in the class.