## Diagonal Matrix

A diagonal matrix is a Matrix of the form

 (1)

where is the Kronecker Delta, are constants, and there is no summation over indices. The general diagonal matrix is therefore Square and of the form
 (2)

Given a Matrix equation of the form

 (3)

multiply through to obtain
 (4)

Since in general, for , this can be true only if off-diagonal components vanish. Therefore, A must be diagonal.

Given a diagonal matrix ,

 (5)