nullity

A Python package for all things linear algebra, built in vanilla python3
Built during MAT-1001 / Linear Algebra at Ashoka University.

Installation

The package is available on PyPI:

pip install nullity

To start using, simply import the package in your Python file:

from nullity import Matrix

Usage

Instantiation

m = Matrix(m, n, *args)

The matrix must be instantiated by first passing in the number of rows (m), then the number of columns (n), and finally the m*n values of the matrix separated by commas.

These values are arranged first in rows and then in columns.
For example:

>>> m = Matrix(2, 3, 1, 2, 3, 4, 5, 6)
>>> print(m)

      1.00       2.00       3.00
      4.00       5.00       6.00

Methods

Function	Output
nrows	Number of rows
ncolumns	Number of columns
is_square	Whether the matrix is square
rref	RREF of the matrix
rank	Rank of the matrix
nullity	Nullity (dimension of the null space) of the matrix
is_invertible	Whether the matrix is invertible
inverse	Inverse of the invertible matrix
rank_factorization	The two rank factorized matrices r and c
row_basis	Basis of the row space
col_basis	Basis of the column space
null_basis	Basis of the null space
transpose	Transpose of the matrix
plu	PLU decomposed matrices p, l, and u
det	Determinant of a square matrix
qr	QR decomposed matrices q and r
charpol	Characteristic polynomial of the matrix
eigenvals	Eigenvalues of the matrix (from numpy)
eigenvecs	Eigenvectors corresponding to the respective eigenvalues
svd	Singular value decomposed matrices u, sigma, and v_transpose

Along with these, addition and multiplication of 2 matrices is also supprted using the inbuilt operators + and * respectively.

Issues

Python's decimal arithmetic often results in incorrect answers. In some cases, approximated output might be sufficient, however in others, errors may be raised.