(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:

$\begin{pmatrix} 0 & 1\\ 1 & 0\\ \end{pmatrix}$ is a 2×2 binary matrix.

A permutation matrix is a binary matrix, all of whose columns and rows each have exactly one nonzero element.
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 binary symmetric matrix with zero diagonal.
A biadjacency matrix is any binary matrix.

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