Binary matrix
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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:
- <math>\begin{pmatrix}
0 & 1\\ 1 & 0\\ \end{pmatrix}<math> 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 Costas array is a special case of a permutation matrix (see article)
- 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.
Properties
The binary idea plays a central role in mathematics, as these two elements are defined in every ring.