I've been searching for a subfield of research to get into and wonder whether random matrix theory could suit me well; it seems like it does, because the stuff I read, and the seminars that I watch online seem to show mathematicians mostly ... doing linear algebra, which I am pretty strong in.
Am I wildly off the mark with the idea that random matrix theory is a lot like doing linear algebra, with random entries in the matrices?
Does random matrix theory have any real-world applications, say, to quantitative finance?
I'm still just beginning to learn about this subfield, so any advice would be greatly appreciated.
I think I am moving away from numerical / analytical partial differential equations, as I don't feel I have strong enough physical reasoning / physics background to do good research in PDEs.