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

\begin{bmatrix} a & b & c \\ d & e & f \\ g & h & i \\ 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

\begin{bmatrix} a \\ b \\ c \end{bmatrix}

Dimension: 3-dimensional vector or $\mathbb{R}^{3}$

$v_{1}=a$

$v_{3}=c$

1-indexed vector:

\begin{bmatrix} y_1 \\ y_2 \\ y_3 \end{bmatrix}

0-indexed vector:

\begin{bmatrix} y_0 \\ y_1 \\ y_2 \end{bmatrix}