Vector Space: An implementation of Vector Space written in both C and Python.

• Why C? God created universe in C.
• Why Python? You know.
• Python code was statically typed and checked using mypy.

Definition and basic properties

• A vector is any object that respects these axioms, In this implementation we assume that they are $\in \mathbb{R}^{n}$

• Dot product is defined as: $$\vec{u} \cdot \vec{w} = \sum_{i}{u_{i}w_{i}} \textit{, where } \vec{u}, \vec{w} \in \mathbb{R}^{n}\text{. In general } V\times V\to F$$

• Norm is defined as: $$||\vec{u}|| = \sqrt{\sum_{i}{|u_{i}|}} = \sqrt{\sum_{i}{u_{i}^{2}}}$$

To Do

• Implement a Cross product.
• Support Vectors $\in \mathbb{C}^{n}$
• Adding Rust implementation, whay? cuz i love Rust.

Requirements

• Python >= 3.11.6
• CC --std=c99 -lm (Clang or GCC).

Running

$ git clone https://github.com/mahmoudElshimi/vector_space
$ cd vector_space
$ python -i vec.py
$ cc --std=c99 -lm -Wall -o vec vec.c && ./vec