A matrix is a rectangular array of numbers. A random matrix can be compared to a Sudoku filled with random numbers. Matrices are part of the equations governing the movements of the particles. In a random matrix there are numbers that are entered randomly, while there are still certain symmetries, for example, you can require that the numbers in the lower left should be a copy of the numbers above the diagonal. This is called a symmetrical matrix.
Kim Splittorff, Associate Professor, Niels Bohr Institute, University of Copenhagen