Status: Active Study Focus: Mathematical Foundations for Deep Learning
This repository documents my progression through the mathematical concepts essential for Artificial Intelligence and Machine Learning. The goal is to move beyond high-level libraries and understand the low-level linear algebra operations that drive modern neural networks.
I am utilizing Python and NumPy to implement these concepts manually, bridging the gap between abstract mathematical theory and executable code.
- Language: Python 3.x
- Core Library: NumPy (for vectorization and matrix manipulation)
- Visualization: Matplotlib / Seaborn
- Environment: Jupyter Notebooks (Anaconda)
Primary Resource: Master Linear Algebra: Theory and Implementation in Code (Mike X Cohen)
- Detailed code-along notebooks:
- Vectors & Spaces (Dot products, spans, basis vectors)
- Matrix Operations (Multiplication, Inverse, Rank)
- Eigendecomposition & SVD
- Least Squares & Projections
- Vectors & Spaces:
- The Span: Deep dive into the infinite reach of linear combinations.
- Algorithmic Verifier: Developed a custom Python tool using
np.linalg.matrix_rankto programmatically validate subspace membership. This ensures that any target vector is mathematically "reachable" before proceeding with downstream model transformations.
- My own sandbox for testing concepts:
- Independent challenges and implementations of algorithms from scratch without relying on pre-built solver functions.
- 3D Subspace Visualization Engine:
- Developed a coordinate-projection tool to visualize how basis vectors define a 2D subspace within 3D space.
- Implemented cross-product normal calculations to render infinite planes using
np.meshgridandplot_surface. - Integrated axis-limit constraints and camera-angle adjustments to ensure clear spatial orientation of vector-plane relationships.
Understanding these concepts is critical for:
- Dimensionality Reduction (PCA, SVD)
- Data Transformation (Basis changes, Linear mappings)
- Optimization (Gradient descent landscapes)
Author: Josh Hasam