Matrices & Vectors

Matrix
Matrix: rectangular array of numbers
Dimension of matrix: number of rows $\times$ number of columns
$A_{ij}$: $i$, $j$ entry in the $i^{th}$ row, $j^{th}$ column

e.g. $$\begin{bmatrix}
a & b & c \newline
d & e & f \newline
g & h & i \newline
j & k & l
\end{bmatrix}$$
dimension: $4\times3$ or $\mathbb{R^{4\times3}}$
$A_{11}=a$
$A_{32}=h$

Vector
Vector: $n\times1$ matrix
$v_{i}$: $i^{th}$ element

e.g. $$\begin{bmatrix}
a \newline
b \newline
c
\end{bmatrix}$$
dimension: 3-dimensional vector or $\mathbb{R^{3}}$
$v_{1}=a$
$v_{3}=c$

1-indexed vector: $$\begin{bmatrix}
y_1 \newline
y_2 \newline
y_3
\end{bmatrix}$$

0-indexed vector: $$\begin{bmatrix}
y_0 \newline
y_1 \newline
y_2
\end{bmatrix}$$