Random matrices are mathematical objects where the entries of the matrix are random variables. They are used to study various phenomena in fields such as statistics, quantum physics, and machine learning. The properties of these matrices can reveal insights about complex systems, especially when analyzing large datasets. The study of random matrices often involves understanding their eigenvalues and eigenvectors, which can provide information about stability and behavior in different contexts. Researchers explore how the distribution of these eigenvalues behaves as the size of the matrix increases, leading to important results in number theory and statistical mechanics.