In particular a symmetric matrix of order n, contains at most different numbers. A diagonal matrix is a symmetric matrix with all of its entries equal to zero except may be the ones on the diagonal. So a diagonal matrix has at most n different numbers. For example, the matrices are diagonal matrices. Identity matrices are examples of diagonal matrices.
Diagonal matrices play a crucial role in matrix theory.
We will see this later on. By induction, one may easily show that for every natural number n . Please post your question on our S.O.S. Mathematics CyberBoard .