NumPy Linear Algebra

A collection of practical NumPy exercises focused on:

• linear algebra
• matrix operations
• broadcasting
• vector projections
• geometric transformations
• 3D visualization
• performance benchmarking

This repository contains hands-on exercises exploring mathematical concepts commonly used in:

• Data Science
• Machine Learning
• Computer Vision
• Robotics
• Scientific Computing
• Game Development

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Technologies

• Python
• NumPy
• Matplotlib

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Topics Covered

1. 3D Data Simulation & Visualization

File: arrays_in_numpy.py

Generate multidimensional coordinate grids using:

• np.linspace()
• np.meshgrid()
• matplotlib

The generated data is visualized as a 3D scatter plot.

Example Visualization

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2. NumPy Broadcasting Rules

File: broadcasting.py

Custom implementation of NumPy broadcasting compatibility checks.

Concepts covered:

• array shapes
• dimension alignment
• broadcasting rules
• shape expansion

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3. Normal Vector Calculation

File: linear_algebra_numpy.py

Calculate a normal vector to a plane defined by three points in 3D space using:

• vector subtraction
• cross product
• vector normalization

Core equation:

[ \vec{n} = \vec{AB} \times \vec{AC} ]

Applications:

• robotics
• computer graphics
• physics simulations

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4. NumPy vs Python Performance Benchmark

File: nparrays.py

Performance comparison between:

• Python lists
• NumPy arrays

Benchmarked operations:

• addition
• multiplication
• exponentiation

Implemented using:

• timeit
• vectorized NumPy operations

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5. Vector Projection

File: vector_projection.py

Projection of one vector onto another using linear algebra formulas.

Projection formula:

[ \mathrm{proj}_{\vec b}\vec a = \frac{\vec a \cdot \vec b}{|\vec b|^2}\vec b ]

Applications:

• cosine similarity
• machine learning
• graphics programming
• physics

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6. Matrix Transformations & Character Movement

File: matrix_transformation.py

Simulation of character movement on a 2D board using:

• homogeneous coordinates
• translation matrices
• matrix multiplication

Translation matrix:

[ \begin{bmatrix} 1 & 0 & dx \ 0 & 1 & dy \ 0 & 0 & 1 \end{bmatrix} ]

Concepts covered:

• geometric transformations
• translation matrices
• board boundary constraints
• matrix multiplication

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7. NumPy Type Casting & Type Promotion

File: type_casting.py

Check whether NumPy operations automatically change array data types.

Concepts covered:

• NumPy dtypes
• type promotion
• array operations
• numerical precision

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Repository Structure

.
├── arrays_in_numpy.py
├── broadcasting.py
├── linear_algebra_numpy.py
├── matrix_transformation.py
├── nparrays.py
├── type_casting.py
├── vector_projection.py
│
├── images/
│   └── 3d_scatter.png
│
└── README.md

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Installation

Clone the repository:

git clone https://github.com/your-username/your-repository.git

Install dependencies:

pip install numpy matplotlib

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Running Examples

Run any exercise individually:

python vector_projection.py

or:

python linear_algebra_numpy.py

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Learning Goals

This repository focuses on building intuition for:

• vectorized computation
• linear algebra with NumPy
• multidimensional arrays
• broadcasting
• geometric transformations
• scientific computing workflows

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Author

Created as part of practical NumPy and linear algebra exercises.