How to Use Markdown for Linear Algebra: Mathematical Notation Examples

See also: How to Start Writing in Markdown

Markdown is a lightweight markup language with plain text formatting syntax. It is often used to format readme files, for writing messages in online discussion forums, and to create rich text using a plain text editor. When it comes to writing mathematical notation, Markdown, in combination with LaTeX or MathJax, is an excellent tool. LaTeX is a high-quality typesetting system that’s widely used for technical and scientific documentation.

In this article, we’ll cover how to use Markdown for linear algebra by providing examples of mathematical notation and their corresponding Markdown code.

Basic Mathematical Notation

To include mathematical notation in Markdown, you typically use a combination of Markdown and LaTeX syntax. Inline mathematical expressions can be enclosed in single dollar signs ($...$), while block mathematical expressions are enclosed in double dollar signs ($$...$$).

1. Matrix Representation

To represent a matrix in Markdown, you can use LaTeX within a block element.

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

Rendered Output: $$ \mathbf{A} = \begin{bmatrix} a_{11} & a_{12} & \cdots & a_{1n}
a_{21} & a_{22} & \cdots & a_{2n}
\cdots & \cdots & \cdots & \cdots
a_{m1} & a_{m2} & \cdots & a_{mn} \end{bmatrix} $$

2. Vector Representation

Vectors can be represented as $\mathbf{v} = \begin{bmatrix} v_{1} \ v_{2} \cdots \ v_{n} \end{bmatrix}$

Vectors can be represented as $\mathbf{v} = \begin{bmatrix} v_{1} \ v_{2} \cdots \ v_{n} \end{bmatrix}$

Or as $\vec{v} = \begin{bmatrix} x \ y \ z \end{bmatrix}$

Or as $\vec{v} = \begin{bmatrix} x \\ y \\ z \end{bmatrix}$

3. Dot Product

The dot product of two vectors $\mathbf{a}$ and $\mathbf{b}$ can be represented as follows:

$$ \mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^{n} a_i b_i $$

$$
\mathbf{a} \cdot \mathbf{b} = \sum_{i=1}^{n} a_i b_i
$$

4. Matrix Multiplication

Matrix multiplication of $\mathbf{A}$ and $\mathbf{B}$:

$$ \mathbf{C} = \mathbf{A} \mathbf{B} $$

where

$$ \mathbf{C_ij} = \sum_{k=1}^{n} \mathbf{A_ik} \mathbf{B_kj} $$

$$
\mathbf{C} = \mathbf{A} \mathbf{B}
$$

where

$$
\mathbf{C_ij} = \sum_{k=1}^{n} \mathbf{A_ik} \mathbf{B_kj}
$$

5. Determinant of a Matrix

The determinant of a 2x2 matrix $\mathbf{A}$:

$$ \det(\mathbf{A}) = \begin{vmatrix} a & b
c & d \end{vmatrix} = ad - bc $$

$$
\det(\mathbf{A}) = \begin{vmatrix}
a & b \
c & d
\end{vmatrix} = ad - bc
$$

Conclusion

Using Markdown with LaTeX for linear algebra notation allows you to create well-formatted, professional-looking documents. The examples provided in this article should give you a solid starting point for writing your own linear algebra documents in Markdown. Whether you’re writing a research paper, a blog post, or documenting a project, these techniques will help you present your mathematical content clearly and effectively.

Remember to use single dollar signs for inline math and double dollar signs for block math, and leverage LaTeX for complex expressions and structures.

Now that you have these tools at your disposal, go ahead and start writing your mathematical documents with ease and precision!