$$ A=\begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...&a_{2n}\\...&...&...&...\\a_{m1}&a_{m2}&...&a_{mn}\end{bmatrix} $$

• If $m=n$, matrix $A$ is square
• If all components equal zero, denote as $0_{m\times n}$

Column vector, or simply just vector ($n\times1$ matrix)

$$ \bold{\vec{x}}=\begin{bmatrix}x_1\\x_2\\...\\x_n\end{bmatrix} $$

• If all components equal zero, denote as $0_n$
  • Or simply $\vec{0}$ if confusion unlikely

Matrices can be added/subtracted

$$ C=A\pm B \\= \begin{bmatrix}a_{11}&a_{12}&...&a_{1n}\\a_{21}&a_{22}&...&a_{2n}\\...&...&...&...\\a_{m1}&a_{m2}&...&a_{mn}\end{bmatrix}\pm \begin{bmatrix}b_{11}&b_{12}&...&b_{1n}\\b_{21}&b_{22}&...&b_{2n}\\...&...&...&...\\b_{m1}&b_{m2}&...&b_{mn}\end{bmatrix}\\ = \begin{bmatrix}a_{11}\pm b_{11} &a_{12}\pm b_{12}&...&a_{1n}\pm b_{1n}\\a_{21}\pm b_{21}&a_{22}\pm b_{22}&...&a_{2n}\pm b_{2n}\\...&...&...&...\\a_{m1}\pm b_{m1}&a_{m2}\pm b_{m2}&...&a_{mn}\pm b_{mn}\end{bmatrix} $$

• A and B have the same number of rows and columns
• $C_{ij} = A_{ij} \pm B_{ij}$ where $ij$ are the indices