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linear-algebra-javascript/README.md

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+# Linear algebra library for JavaScript  
+
+This library contains some useful classes and functions for dealing with linear algebra in JavaScript.  
+The library was orginal written in **TypeScript** and then compiles into pure JavaScript.  
+
+---
+
+## Overview  
+
+- class Vector : This class represents a vector of arbitray size and operations on it.  
+    - constructor Vector(N) : creates a zero vector of size N   
+    - constructor Vector(N, components) : creates a vector of size N with the given components.   
+    - createUnitBasis(pos) : converts this vector in a unit basis vector and returns it.  
+    - component(pos) : returns the specified component (indexing at 0)  
+    - changeComponent(pos, value) : change the specified component.  
+    - toString() : returns a string representation of this vector.  
+    - size() : returns the size of the vector. (not the eulidean length!)  
+    - eulideanLength() : computes the eulidean length of this vector.  
+    - add(other) : vector addition, returns the rersult.  
+    - sub(other) : vector subtraction, returns the rersult.  
+    - dot(other) : computes the dot-product and returns it.  
+    - scalar(s)  : scalar (s) multiplication. returns the result.  
+    - norm() : normalizes this vector and returns it.  
+    - equal(other) : returns true if the vectors are equal, otherwise false.  
+
+- function unitBasisVector(N,pos) : returns a unit basis vector of size N with a One on position 'pos'  
+- function randomVectorInt(N,a,b) : returns a random vector with integer components (between 'a' and 'b') of size N.  
+- function randomVectorFloat(N,a,b) : returns a random vector with floating point components (between 'a' and 'b') of size N.    
+
+- class Matrix : This class represents a matrix of arbitrary size and operations on it.  
+    - constructor(rows, cols) : creates a zero matrix of dimension rows x cols.  
+    - constructor(rows, cols, components) : creates a matrix with fix numbers of dimension rows x cols.  
+    - component(x,y) : returns the specified component.  
+    - changeComponent(x,y,value) : changes the specified component with the new value 'value'.  
+    - toString() : returns a string representation of this matrix.  
+    - dimension() : returns the dimension of this matrix as number arras [rows,cols].  
+    - add(other) : returns the result of the matrix addition.  
+    - equal(other) : returns true if the matrices are equal, otherwise false.  
+    - scalar(c) : returns the result of the matrix-scalar multiplication.  
+---
+
+## Documentation  
+
+The module is well documented in its source code. Look in the TypeScript file ```la_lib.ts```.  
+
+---
+
+## Usage  
+
+You will find the library in the **src** directory its called ```la_lib.js```. You simply need to  
+include this library in your project **(you don't install anything)**. After that:  
+
+```js
+    var x = LinearAlgebra.Vector(...);
+```  
+
+The namespace LinearAlgebra contains useful classes and functions for dealing with linear algebra under JavaScript.  
+
+Some examples:  
+
+```js
+// ---------------------------- Examples ------------------------------------------
+
+// creates vectors 
+var x = new LinearAlgebra.Vector(5, [1, 2, 3, 4, 5]);
+var y = new LinearAlgebra.Vector(5, [1, 2, 3, 4, 5]);
+
+// prints size of the vector
+console.log(x.size()); // ==> 5
+
+// changes the 2-th component with 7
+//x.changeComponent(2,7);
+
+// print the 2-th component.
+console.log(x.component(2)); // ==> 3
+
+// prints the full vector as string.
+console.log(x.toString()); // ==> (1,2,3,4,5)
+
+// vector addition
+console.log(x.add(y).toString()); // ==> (2,3,6,8,10)
+
+//console.log(x.createUnitBasis(1).toString());
+
+// computes the dot-product
+console.log(x.dot(y)); // ==> 55
+
+// computes and prints the scalar-product
+console.log(x.scalar(5).toString()); // ==> (5,10,15,20,25)
+
+// creates a unit basis vector
+console.log(LinearAlgebra.unitBasisVector(3, 0).toString()); // ==> (1,0,0)
+
+// creates random vectors
+console.log(LinearAlgebra.randomVectorInt(3, 0, 5).toString());
+console.log(LinearAlgebra.randomVectorFloat(3, 0, 5).toString());
+```  
+
+---
+
+## Tests  
+
+Go in the directory of the project and type in:  
+```npm install```  
+```npm test```  
+The test-suite use the JavaScript test-framework **mocha**.  
+
+---
+
+## Contributing  
+
+You can contribute to this project. Feel free and pull request some new features or documention.   
+**TODO:** Global functions for special matrices.  
+**TODO:** Documention of the classes and functions.