> For the complete documentation index, see [llms.txt](https://tony-ng-1.gitbook.io/matrices-and-linear-algebra-fundamentals/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://tony-ng-1.gitbook.io/matrices-and-linear-algebra-fundamentals/master.md).

# Introduction to Matrices (Pt. 1)

## Why are Matrices important?

Wait, what, are we learning math all-over again!? 👻

![](https://media1.giphy.com/media/aHv7TBImivdAI/giphy.gif)

Maybe a good way to start off this GitBook is through the words of this man, a lecturer of MIT, Gilbert Strang. 

{% embed url="<https://www.youtube.com/watch?v=YeyrH-Oc2p4>" %}

I highly recommend watch his videos first, but will too humbly summarize his discussions.

## Matrices

*Matrices* are (good for me, people with OCD lol) neat.&#x20;

It offers both a tidy way to&#x20;

1. Represent **dimensions**, and
2. A nifty way to **transform** data as well.

They are essentially

{% hint style="success" %}

* *Numbers* (and sometimes algebra), that are
* Spaced out neatly in *rows and columns*, whom are
* Arranged in a *rectangular* (sometimes brackets or straight-lines lol❓❓❓) array
  {% endhint %}

This eases the representation of multiple *dimensions*, and also offers a *transparent, verifiable* way to demonstrate *transformation process* of data (addressing algorithmic bias).

Dimensions are equivalent often input variables, and if you are unsure what it is, don't worry as of yet! 😉 It is merely a term used in **machine learning** to predict *output variables,* *general patterns and trends,* or for *reinforcement learning*.

> For example, there may be numerous input variables that may go into a supposed model created for the whole purpose of predicting an output variable "HDB housing price", where these could range from substantial to trivial factors such as *location, type of flat (HDB flats or EC), amount of rooms, the amenities available, years of lease remaining, noise* factor (if it close to an air-base or airport), and etc.

Currently, matrices are widely used in:

* Inputs (possibly output) of machine learning (specifically deep learning / neural networks)&#x20;
* Term-document matrix in Natural Language Processing (NLP)

## References

```
https://towardsdatascience.com/linear-algebra-for-deep-learning-f21d7e7d7f23
https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-ditributive-property/a/distributive-property-explained
https://www.analyticsvidhya.com/blog/2017/05/comprehensive-guide-to-linear-algebra/
https://www.youtube.com/watch?v=kYB8IZa5AuE
https://www.kaggle.com/mjbahmani/linear-algebra-for-data-scientists
https://docs.scipy.org/doc/numpy/reference/routines.linalg.html
https://www.quantstart.com/articles/scalars-vectors-matrices-and-tensors-linear-algebra-for-deep-learning-part-1/
https://www.youtube.com/watch?v=J7DzL2_Na80&t=192s
```

### **More on the next page ⏭**