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1 Examples

Examples of binary matrices are numerous:

is a 2×2 binary matrix.

• 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.

2 Properties

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