# (0,1)-matrix

A **binary matrix** or **(0,1)-matrix** is a matrix whose entries are all either zero or one.

## Examples

Examples of binary matrices are numerous:

- A permutation matrix is a binary matrix whose columns and rows sum up to one.
- A design matrix in analysis of variance is a binary matrix with constant row sums.
- An adjacency matrix in graph theory is a matrix whose rows and columns represent the vertices and whose entries represent the edges of the graph. The adjacency matrix of a simple, undirected graph is a symmetric binary matrix.

## Properties

The binary idea plays a central role in mathematics, as these two elements are defined in every ring.