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 offdiagonal components vanish.
Therefore, A must be diagonal.
Given a diagonal matrix
,

(5) 
See also Matrix, Triangular Matrix, Tridiagonal Matrix
References
Arfken, G. Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 181184 and 217229, 1985.
© 19969 Eric W. Weisstein
19990524