Bump version number, rename project, implement lib into example

The project was renamed to better reflect it's purpose: Being able
to handle different excercises in linear algebra and not only the
Gram-Schmidt Processes:
	https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process

Cargo.toml

 [package]
-name = "orthonormalizing"
-version = "0.1.0"
+name = "lin_b"
+version = "0.2.0"
 authors = ["Andre Julius <norom@jimileibniz.de>"]
 
 [dependencies]

src/main.rs

-extern crate orthonormalizing;
-use orthonormalizing::math::complex_number::ComplexNumber;
+extern crate lin_b;
+use lin_b::math::vector::Vector;
+use lin_b::math::complex_number::ComplexNumber;
 
 fn main() {
-    let a = ComplexNumber::new(1f64, 0f64);
-    let b = ComplexNumber::new(1f64, 1f64);
-    println!("a={:?}, b={:?}", a, b);
-    println!("a+b={:?}", a+b);
+    let v1 = Vector::new(vec![
+        ComplexNumber::new(1.0, 0.0),
+        ComplexNumber::new(0.0, 1.0),
+        ComplexNumber::new(1.0, 0.0),
+        ComplexNumber::new(0.0, 1.0),
+    ]);
+    let v2 = Vector::new(vec![
+        ComplexNumber::new(1.0, 0.0),
+        ComplexNumber::new(0.0, 1.0),
+        ComplexNumber::new(0.0, 0.0),
+        ComplexNumber::new(0.0, 0.0),
+    ]);
+    let v3 = Vector::new(vec![
+        ComplexNumber::new(0.0, 0.0),
+        ComplexNumber::new(0.0, 0.0),
+        ComplexNumber::new(1.0, 0.0),
+        ComplexNumber::new(2.0, 0.0),
+    ]);
+    println!("Starting vectors:");
+    println!("v1 = {}", v1);
+    println!("v2 = {}", v2);
+    println!("v3 = {}", v2);
+
+    let u1 = v1.clone();
+    let u2 = v2.clone() - u1.orthogonal_projection(&v2);
+    let u3 = v3.clone() - u1.orthogonal_projection(&v3) - u2.orthogonal_projection(&v3);
+    println!("Orthogonalized vectors:");
+    println!("u1 = {}", u1);
+    println!("u2 = {}", u2);
+    println!("u3 = {}", u3);
+
+    let e1 = u1.clone() / ComplexNumber::new(u1.norm(), 0.0);
+    let e2 = u2.clone() / ComplexNumber::new(u2.norm(), 0.0);
+    let e3 = u3.clone() / ComplexNumber::new(u3.norm(), 0.0);
+    println!("Orthonormalized vectors");
+    println!("e1 = {}", e1);
+    println!("e2 = {}", e2);
+    println!("e3 = {}", e3);
+
 }