> For the complete documentation index, see [llms.txt](https://changsin.gitbook.io/math/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://changsin.gitbook.io/math/linear-algebra/what-are-vectors-and-matrices.md).

# What are vectors and matrices?

### What are vectors

   In the simplest form, a vector is just a list of number v = \[1, 2, 3]. Mathematically speaking, the correct definition is that [a vector](https://en.wikipedia.org/wiki/Vector_\(mathematics_and_physics\)) is an element in vector space. Concretely, a vector is said to have a magnitude and a direction. For a vector v = \[a, b], the magnitude is:

$$
|v| = \sqrt{a^2 + b^2}
$$

For the direction