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feat(array): replaced LaTeX math delimiters (\[ and \]) with dollar s…
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…igns ($) for inline math expressions."
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0xii00 committed Aug 12, 2024
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Expand Up @@ -106,22 +106,22 @@ For example, in edge detection, a filter might emphasize the difference between
#### Example 1: 2D Matrix (2x3 Matrix)
A 2D matrix is essentially a grid of numbers arranged in rows and columns. For example, a 2x3 matrix (2 rows and 3 columns) can be represented as:

\[
$
\mathbf{A} =
\begin{pmatrix}
1 & 2 & 3 \\
4 & 5 & 6
\end{pmatrix}
\]
$

This matrix has:
- 2 rows: \([1, 2, 3]\) and \([4, 5, 6]\)
- 3 columns: \([1, 4]\), \([2, 5]\), and \([3, 6]\)
- 2 rows: $[1, 2, 3]$ and $[4, 5, 6]$
- 3 columns: $[1, 4]$, $[2, 5]$, and $[3, 6]$

#### Example 2: 3D Matrix (2x2x3 Tensor)
A 3D matrix (or tensor) can be thought of as a stack of 2D matrices. For example, a 2x2x3 tensor can be represented as:

\[
$
\mathbf{B} =
\begin{pmatrix}
\begin{pmatrix}
Expand All @@ -133,32 +133,32 @@ A 3D matrix (or tensor) can be thought of as a stack of 2D matrices. For example
10 & 11 & 12
\end{pmatrix}
\end{pmatrix}
\]
$

This tensor can also be visualized as two 2x3 matrices stacked along a third dimension.

#### Example 3: 2D Shape (Rectangle)

A 2D shape, such as a rectangle, can be described using its vertices (corner points) in a 2D coordinate system:

- Let the vertices be \((0, 0)\), \((4, 0)\), \((4, 3)\), and \((0, 3)\).
- Let the vertices be $(0, 0)$, $(4, 0)$, $(4, 3)$, and $(0, 3)$.

This rectangle can be represented as a set of coordinate pairs:

\[
$
\text{Vertices} = \{(0, 0), (4, 0), (4, 3), (0, 3)\}
\]
$

#### Example 4: 3D Shape (Cube)

A 3D shape, such as a cube, can be described using its vertices in a 3D coordinate system. For a cube of side length 2 centered at the origin, the vertices are:

\[
$
\text{Vertices} = \{
(-1, -1, -1), (-1, -1, 1), (-1, 1, -1), (-1, 1, 1), \\
(1, -1, -1), (1, -1, 1), (1, 1, -1), (1, 1, 1)
\}
\]
$

This cube can be visualized as having 8 vertices, 12 edges, and 6 faces.

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