linearean 0.1.1

A pure-Python linear algebra package with matrices, vectors, and manual numerical algorithms.

linearean

A small linear algebra package written from scratch in pure Python. It provides matrix and vector data structures, manual Gaussian-elimination based routines, power iteration, and extensions for complex-valued linear algebra, tensor products, and Markov-chain checks.

The package intentionally avoids high-level numerical libraries so the core algorithms are easy to read and study.

Features

• Matrix and Vector classes with dimension validation.
• Operator overloading for +, -, scalar *, and matrix multiplication with @.
• Determinants and inverses using manual Gaussian elimination / Gauss-Jordan elimination with partial pivoting.
• Linear solves, rank, reduced row echelon form, trace, transpose, and norms.
• Power iteration for the dominant eigenvalue and eigenvector.
• Complex conjugate transpose, Hermitian/unitary checks, Kronecker products, tensor powers, and stochastic-matrix validation.

Quick start

from linearean import Matrix, Vector, power_iteration
from linearean.extensions import kronecker_product, is_stochastic

A = Matrix([[2, 1], [5, 3]])
B = Matrix([[1, 0], [0, 1]])
v = Vector([1, 2])

print(A + B)
print(A @ v)
print(A.determinant())
print(A.inverse())

eigenvalue, eigenvector = power_iteration(A)
print(eigenvalue, eigenvector)

coin = Matrix([[0.5, 0.5], [0.5, 0.5]])
print(is_stochastic(coin))

system = kronecker_product(B, B)
print(system)

Development

Run tests with:

python -m unittest discover

Install locally in editable mode with:

python -m pip install -e .