A custom Linear Algebra Library in Julia designed to implement both core and advanced operations from scratch. This project serves as an educational and performance-focused foundation for numerical computing and future applications in areas such as machine learning and physics.
- Matrix and Vector types
- Addition, Subtraction
- Scalar and Matrix Multiplication
- Transpose
- Dot and Cross Product
- Identity and Zero Matrices
- Gaussian Elimination
- LU Decomposition
- Back and Forward Substitution
- Matrix Inversion
- Determinant Calculation
- Condition Number
- Rank of a Matrix
- Null Space / Kernel
- Column and Row Space
- Orthogonalization (Gram-Schmidt)
- Orthonormal Basis
- Vector Projection
- QR Decomposition
- Cholesky Decomposition
- Eigenvalues and Eigenvectors
- Singular Value Decomposition (SVD)
- Julia Multiple Dispatch and Type Stability
- Optimization with @inbounds, @simd, etc.
- Unit Testing Suite
- Full Julia Package Support
- Documentation with Documenter.jl
- Linear Regression via Normal Equation
- Least Squares Solver
- Principal Component Analysis (PCA)
- Graph Laplacian Matrix