Integer Matrix

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only (0,1) as entries (e.g., adjacency matrix, Frobenius-König theorem, Gale-Ryser theorem, Hadamard's maximum determinant problem, hard square entropy constant, identity matrix, incidence matrix, Lam's problem), and those having (-1,0,1) as entries (e.g., alternating sign matrix, C-matrix).

The zero matrix could be considered a degenerate case of an integer matrix. Integer matrices are sometimes also called "integral matrices," although this usage should be deprecated due to its confusing use of the term "integral" as an adjective.

See also

Alternating Sign Matrix, (-1,0,1)-Matrix, (-1,1)-Matrix, (0,1)-Matrix, C-Matrix, Complex Matrix, Fifteen Theorem, Frobenius-König Theorem, Gale-Ryser Theorem, Hadamard's Maximum Determinant Problem, Hadamard Matrix, Hafner-Sarnak-McCurley Constant, Hard Square Entropy Constant, Identity Matrix, Incidence Matrix, Integer-Matrix Form, Interspersion, Lam's Problem, Mortal, Mortality Problem, Real Matrix, Smith Normal Form, Special Matrix, Unit Matrix, Zero Matrix

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Cite this as:

Weisstein, Eric W. "Integer Matrix." From MathWorld--A Wolfram Web Resource.

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