nullity

A package for all things linear algebra


Keywords
linear, algebra, linalg, lin-alg, linearalgebra, eigen, eigenvalue, eigenvector, nullity, null, space, rank
License
GPL-3.0
Install
pip install nullity==0.0.3

Documentation

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.