Diagonal Matrix

A diagonal matrix is an n x n matrix with every off diagonal element equal to zero.

This is often written showing just the diagonal elements and the upper-right and lower-left corners with a 0

If we have two matrices such that:

 

Then:

If each element , then

The eigenvalues of D are its main diagonal elements, d₁, d₂, d₃, ......d_n

See also: Hankel Matrix, Matrix, Trace.

Further reading:
• Matrices: Theory and Applications (Graduate Texts in Mathematics), Denis Serre, Springer-Verlag Berlin and Heidelberg GmbH & Co. KG