Binary matrix

In mathematics, particularly matrix theory, a binary matrix is either (usually) a matrix whose entries are zeros or ones belonging to any field (this is also called a (0,1)-matrix), or (especially in matroid theory) a matrix whose elements belong to the two-element Galois field GF(2).

It is not difficult to see that the number of m×n binary matrices is equal to 2^mn, and is thus finite.

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 (0,1)-matrix, all of whose columns and rows each have exactly one nonzero element.
  • A Costas array is a special case of a permutation matrix
• An incidence matrix in combinatorics and finite geometry has ones to indicate incidence between points (or vertices) and lines of a geometry, blocks of a block design, or edges of a graph (mathematics)
• A design matrix in analysis of variance is a (0,1)-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.
• The biadjacency matrix of a simple, undirected bipartite graph is a (0,1)-matrix, and any (0,1)-matrix arises in this way.