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Title: Integer Matrix -- from Wolfram MathWorld

Open Graph Title: Integer Matrix -- from Wolfram MathWorld

X Title: Integer Matrix -- from Wolfram MathWorld

Description: 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...

Open Graph Description: 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...

X Description: 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...

Opengraph URL: https://mathworld.wolfram.com/IntegerMatrix.html

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Domain: mathworld.wolfram.com

DC.TitleInteger Matrix
DC.CreatorWeisstein, Eric W.
DC.DescriptionA 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...
DC.Subject15B36
DC.RightsCopyright 1999-2026 Wolfram Research, Inc. See https://mathworld.wolfram.com/about/terms.html for a full terms of use statement.
DC.Formattext/html
DC.Identifierhttps://mathworld.wolfram.com/IntegerMatrix.html
DC.Languageen
DC.PublisherWolfram Research, Inc.
DC.Relation.IsPartOfhttps://mathworld.wolfram.com/
DC.TypeText
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og:typewebsite
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Integer Matriceshttps://mathworld.wolfram.com/topics/IntegerMatrices.html
matrixhttps://mathworld.wolfram.com/Matrix.html
Hadamard matrixhttps://mathworld.wolfram.com/HadamardMatrix.html
(0,1)-matriceshttps://mathworld.wolfram.com/01-Matrix.html
adjacency matrixhttps://mathworld.wolfram.com/AdjacencyMatrix.html
Frobenius-König theoremhttps://mathworld.wolfram.com/Frobenius-KoenigTheorem.html
Gale-Ryser theoremhttps://mathworld.wolfram.com/Gale-RyserTheorem.html
Hadamard's maximum determinant problemhttps://mathworld.wolfram.com/HadamardsMaximumDeterminantProblem.html
hard square entropy constanthttps://mathworld.wolfram.com/HardSquareEntropyConstant.html
identity matrixhttps://mathworld.wolfram.com/IdentityMatrix.html
incidence matrixhttps://mathworld.wolfram.com/IncidenceMatrix.html
Lam's problemhttps://mathworld.wolfram.com/LamsProblem.html
alternating sign matrixhttps://mathworld.wolfram.com/AlternatingSignMatrix.html
C-matrixhttps://mathworld.wolfram.com/C-Matrix.html
zero matrixhttps://mathworld.wolfram.com/ZeroMatrix.html
integralhttps://mathworld.wolfram.com/Integral.html
Alternating Sign Matrixhttps://mathworld.wolfram.com/AlternatingSignMatrix.html
(-1,0,1)-Matrixhttps://mathworld.wolfram.com/-101-Matrix.html
(-1,1)-Matrixhttps://mathworld.wolfram.com/-11-Matrix.html
(0,1)-Matrixhttps://mathworld.wolfram.com/01-Matrix.html
C-Matrixhttps://mathworld.wolfram.com/C-Matrix.html
Complex Matrixhttps://mathworld.wolfram.com/ComplexMatrix.html
Fifteen Theoremhttps://mathworld.wolfram.com/FifteenTheorem.html
Frobenius-König Theoremhttps://mathworld.wolfram.com/Frobenius-KoenigTheorem.html
Gale-Ryser Theoremhttps://mathworld.wolfram.com/Gale-RyserTheorem.html
Hadamard's Maximum Determinant Problemhttps://mathworld.wolfram.com/HadamardsMaximumDeterminantProblem.html
Hadamard Matrixhttps://mathworld.wolfram.com/HadamardMatrix.html
Hafner-Sarnak-McCurley Constanthttps://mathworld.wolfram.com/Hafner-Sarnak-McCurleyConstant.html
Hard Square Entropy Constanthttps://mathworld.wolfram.com/HardSquareEntropyConstant.html
Identity Matrixhttps://mathworld.wolfram.com/IdentityMatrix.html
Incidence Matrixhttps://mathworld.wolfram.com/IncidenceMatrix.html
Integer-Matrix Formhttps://mathworld.wolfram.com/Integer-MatrixForm.html
Interspersionhttps://mathworld.wolfram.com/Interspersion.html
Lam's Problemhttps://mathworld.wolfram.com/LamsProblem.html
Mortalhttps://mathworld.wolfram.com/Mortal.html
Mortality Problemhttps://mathworld.wolfram.com/MortalityProblem.html
Real Matrixhttps://mathworld.wolfram.com/RealMatrix.html
Smith Normal Formhttps://mathworld.wolfram.com/SmithNormalForm.html
Special Matrixhttps://mathworld.wolfram.com/SpecialMatrix.html
Unit Matrixhttps://mathworld.wolfram.com/UnitMatrix.html
Zero Matrixhttps://mathworld.wolfram.com/ZeroMatrix.html
28https://www.wolframalpha.com/input/?i=28
ellipse with equation (x-2)^2/25 + (y+1)^2/10 = 1https://www.wolframalpha.com/input/?i=ellipse+with+equation+%28x-2%29%5E2%2F25+%2B+%28y%2B1%29%5E2%2F10+%3D+1
limit tan(t) as t->pi/2 from the lefthttp://www.wolframalpha.com/input/?i=limit+tan%28t%29+as+t-%3Epi%2F2+from+the+left
Weisstein, Eric W.https://mathworld.wolfram.com/about/author.html
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https://mathworld.wolfram.com/IntegerMatrix.htmlhttps://mathworld.wolfram.com/IntegerMatrix.html
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