# Random matrix theory and research - a lot like doing linear algebra?

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?

• Random matrices are mathematically interesting. The eigenvalue distribution, for instance, is a standard problem. You might give yourself that problem to solve for $P(\lambda)$ for a random $2 \times 2$ matrix $M$ with the matrix elements $M_{i,j} \sim N(0,1)$. Practically speaking, an additional constraint makes the problem much more interesting, like positive definiteness. For instance, a common practical problem involves making small random perturbations to covariance matrices (guaranteed to be positive definite) for applications in modeling multivariate normal distributions. – Peter Leopold Jul 23 '19 at 12:35