Notations at Math for ML

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Basic Notation

Capital letters represent matrices: $A, B, C$
Lowercase letters represent vectors: $u, v, w$
Matrix $A$ has $m$ rows and $n$ columns: $A \in \mathbb{R}^{m \times n}$
The transpose of matrix $A$: $A^T$
The transpose of vector $v$: $v^T$
The inverse of matrix $A$: $A^{-1}$
The determinant of matrix $A$: $\det(A)$
Matrix multiplication of matrices $A$ and $B$: $AB$
Dot product of vectors $u$ and $v$: $u \cdot v$, $\langle u, v \rangle$

Sets and Spaces

The set of real numbers: $\mathbb{R}$ (e.g., $-0.642, 2, 3.456 \in \mathbb{R}$)
The set of two-dimensional vectors: $\mathbb{R}^2$ (e.g.,$v = \begin{bmatrix} 1 \\ 3 \end{bmatrix} \in \mathbb{R}^2$ )
The set of $n$-dimensional vectors: $\mathbb{R}^n$
Vector $v$ is an element of $\mathbb{R}^2$: $v \in \mathbb{R}^2$

Vector Norms

$L1$-norm of a vector: $|v|_1$
$L2$-norm of a vector: $|v|_2$, $|v|$, $||v||$

Transformations

Transformation $T$ of a vector $v \in \mathbb{R}^2$ into the vector $w \in \mathbb{R}^3$:
$ T: \mathbb{R}^2 \rightarrow \mathbb{R}^3, \, T(v) = w $

Acknowledgement

Using Gemini 1.5 Complex Advanced support in LaTeX work.

Update

22/12/24: Update a bit of information