| 1 | ---
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| 2 | title: algebra
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| 3 | ---
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| 4 |
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| 5 | > Vectors, Matrices, Tensors
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| 6 |
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| 7 | {% include node_badges.md package='algebra' %}
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| 8 |
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| 9 |  
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| 10 |
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| 11 | ## Installation
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| 12 |
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| 13 | With [npm](https://npmjs.org/) do
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| 14 |
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| 15 | ```
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| 16 | $ npm install algebra
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| 17 | ```
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| 18 |
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| 19 | With [bower](http://bower.io/) do
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| 20 |
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| 21 | ```bash
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| 22 | $ bower install algebra
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| 23 | ```
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| 24 |
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| 25 | ## Description
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| 26 |
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| 27 | I'm implementing matrices and vectors on few algebra fields (Reals, Complexes etc.) following Micheal Artin's "Algebra", which was my book at [Università Degli Studi di Genova](http://www.dima.unige.it).
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| 28 |
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| 29 | My goal is to provide users with the feature of creating their own algebra field and building vector spaces, matrices and tensors on it.
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| 30 |
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| 31 | Suppose for example the set of strings with the concatenation operator, it could be extended to a group and maybe to a field and build "matrices of strings" or probably in the future ... "strings of matrices" (I had an intuition about a composition law for UTF-8 chars).
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| 32 |
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| 33 | ## Motivation
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| 34 |
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| 35 | Why implement *algebra* with JavaScript? This is my first Node project, I started it cause I wanted to learn Node ... and I really like it!
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| 36 | I was thinking about
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| 37 |
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| 38 | > How to implement an algebra field, like Real and Complex numbers and its elements?
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| 39 |
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| 40 | Do you need to implement first the *Field* class or the *Element* class? In *Algebra* you start defining a *Group*, without specifing its elements; then you define a *Field* adding multiplication operator. Can the programming way be the same as the mathematician way?
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| 41 | I was looking at the answer coding this package.
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| 42 |
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| 43 | Another motivation was to implements something similar to a Tensor, that is like a multi dimensional array, but I could not find any package with that spirit of adventure.
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| 44 |
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| 45 | ## Features
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| 46 |
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| 47 | * Expressive api
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| 48 | * Vectors and Vector Spaces
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| 49 | * Invertible Matrices and the General Linear Group
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| 50 | * [Tensors](http://en.wikipedia.org/wiki/Tensor): scalars, vectors and matrices are also implemented as tensors.
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| 51 | * Algebra over custom fields
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| 52 |
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| 53 | ## Examples
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| 54 |
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| 55 | Begin with [algebra quick start](//g14n.info/algebra/examples/quick-start).
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| 56 |
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| 57 | Other examples:
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| 58 |
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| 59 | * [Real number](//g14n.info/algebra/examples/real-number)
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| 60 | * [Real vector](//g14n.info/algebra/examples/real-vector)
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| 61 | * [Complex number](//g14n.info/algebra/examples/complex-number)
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| 62 | * [Custom field](//g14n.info/algebra/examples/custom-field)
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