Matrix and Matrix multiplication

1. Overview

2. Description

2.1 Notation

$$\boldsymbol{A}=\begin{pmatrix} 1 & 6 & 0 \\  7 & 2 & 4 \\  4 & 1 & 1 \end{pmatrix}$$

$$a_{1,2}=6$$

2.2 Block matrices

$$\boldsymbol{A}=\begin{pmatrix} \boldsymbol{D} & \boldsymbol{0} \\  \boldsymbol{1} & \boldsymbol{D} \end{pmatrix}=\begin{pmatrix} 3 & 0 & 0 & 0\\  0 & 4 & 0 & 0\\  1 & 1 & 3 & 0\\  1 & 1 & 0 & 4 \end{pmatrix}$$

$\boldsymbol{D}=\begin{pmatrix} 3 & 0\\  0 & 4 \end{pmatrix}$, $\boldsymbol{0}=\begin{pmatrix} 0 & 0\\  0 & 0 \end{pmatrix}$, $\boldsymbol{1}=\begin{pmatrix} 1 & 1\\  1 & 1 \end{pmatrix}$

2.3 Matrix size

2.4 Diagonal and off-diagonal

2.5 Matrix dimensionality

2.6 Matrix hyper-dimensionality

3. Matrix multiplication

4. Symmetric multiplication

Symmetric matrix x Symmetric matirx $\neq$ Symmetric matirx, but special cases below meet that condition:

4. References

https://en.wikipedia.org/wiki/Matrix_(mathematics)