Matrix diagonalization is a process that transforms a square matrix into a diagonal form, where all non-diagonal elements are zero. This is useful because diagonal matrices are easier to work with, especially for computations like raising a matrix to a power or solving systems of linear equations. A matrix can be diagonalized if it has enough linearly independent eigenvectors. To diagonalize a matrix, one typically finds its eigenvalues and eigenvectors. The matrix is expressed as the product of three matrices: the original matrix is equal to the product of a matrix of its eigenvectors, a diagonal matrix of its eigenvalues, and the inverse of the eigenvector matrix. This technique simplifies many mathematical operations.