What is a diagonal matrix?

A diagonal matrix is a square matrix that has non-zero elements only in the diagonal that runs from the top left to the bottom right. A diagonal matrix is also a symmetrical matrix.

A diagonal matrix in which all the diagonal elements are equal is called a scalar matrix. This kind of matrix is equal to the identity matrix multiplied by a scalar. Diagonal matrices have much simpler rules of addition and multiplication than general square matrices. Adding or multiplying two diagonal matrices results in another diagonal matrix, with each element equal to the sum or product of the corresponding elements in the original matrices.