xiangzejun / binary_matrix

Calculate Rank, determinant and inverse matrix of a binary matrix (matrix on $F_2$).

Binary Matrix Computation

What is binary matrix?

Binary matrix is a matrix with all the entries restriced in $$$\mathbb{F}_2$$$ which is the finite field with only two elements 0 and 1. Thus, each entry of the matrix can only take the value 0 and 1.

The arithmetic operations on finite field $$$ \mathbb{F}_2 $$$ follow the rules:

• $$$ 0 + 0 = 0, 0 + 1 = 1, 1 + 0 = 1, 1 + 1 = 0 $$$
• $$$ 0 \times 0 = 0, 0 \times 1 = 1, 1\times 0 = 0, 1\times 1 = 1 $$$

What is this module about?

This project contains a module binmatrix.py. This module computes some properties of binary matrices. To be Specific:

1. Compute the Rank of the given binary matrix.
2. Compute the determinant of the given binary matrix if this matrix is a square matrix.
3. Compute the inverse of a given binary matrix if this matrix is a square matrix and full rank.

All the arithmetic operations are on the finite field $$$\mathbb{F}_2$$$. test.py tests the module by a given binary matrix.

How to use the module?

This module defines a python class class BinMatrix:. If m is a binary matrix, you can instantiate a BinMatrix object by matrix = BinMatrix(m). Then you can compute:

1. matrix.rank() returns the Rank of the binary matrix.
2. matrix.det() returns the determinant of the binary matrix.
3. matrix.inv() returns the inverse of the binary matrix.