Diagonal Matrices

A matrix $D=[d_{ij}]\in M_{n\times n}(\mathbb{R})$ is diagonal if:

• $d_{ij}=0$ when $i\ne j$
• The determinant of a diagonal matrix is $\det (D)=d_{11}{d}_{22}\dots d_{nn}$

Niceness of Diagonal Matrices

The formula for a matrix that is all diagonal will be $d_{11}\ast d_{22}\ast \cdots \ast d_{nn}$ always.