Diagonal Matrix

A Square Matrix is a Diagonal Matrix if the only nonzero elements are on the northwest to southeast diagonal.

$\begin{bmatrix} 2.54 && 0 && 0 && 0 \\ 0 && 2.54 && 0 && 0 \\ 0 && 0 && 2.54 && 0 \\ 0 && 0 && 0 && 1 \end{bmatrix}$

Identity Matrix for Three Dimensions:

$\begin{bmatrix} 1 && 0 && 0 \\ 0 && 1 && 0 \\ 0 && 0 && 1 \end{bmatrix}$

Appendix A

The matrix multiplication of two diagonal matrices is commutative:

$\begin{bmatrix} a_{11} && 0 && 0 \\ 0 && a_{22} && 0 \\ 0 && 0 && a_{33} \end{bmatrix} \begin{bmatrix} b_{11} && 0 && 0 \\ 0 && b_{22} && 0 \\ 0 && 0 && b_{33} \end{bmatrix} = \begin{bmatrix} a_{11}b_{11} && 0 && 0 \\ 0 && a_{22}b_{22} && 0 \\ 0 && 0 && a_{33}b_{33} \end{bmatrix}$

$\begin{bmatrix} b_{11} && 0 && 0 \\ 0 && b_{22} && 0 \\ 0 && 0 && b_{33} \end{bmatrix} \begin{bmatrix} a_{11} && 0 && 0 \\ 0 && a_{22} && 0 \\ 0 && 0 && a_{33} \end{bmatrix} = \begin{bmatrix} b_{11}a_{11} && 0 && 0 \\ 0 && b_{22}a_{22} && 0 \\ 0 && 0 && b_{33}a_{33} \end{bmatrix}$

$\begin{bmatrix} a_{11}b_{11} && 0 && 0 \\ 0 && a_{22}b_{22} && 0 \\ 0 && 0 && a_{33}b_{33} \end{bmatrix} = \begin{bmatrix} b_{11}a_{11} && 0 && 0 \\ 0 && b_{22}a_{22} && 0 \\ 0 && 0 && b_{33}a_{33} \end{bmatrix}$

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