In linear algebra, a diagonal matrix is a particular type of square matrix. The main-diagonal may contain any real values, but the elements that do not coincide with the main-diagonal must all be zeros. In particular, given any ring with additive identity given by , a matrix (an -by- matrix whose entries are elements of ) is said to be a diagonal matrix if for any and such that , , where denotes the -th entry. An identity matrix is a special case of the diagonal matrix. Diagonal matrices are very useful computationally, since