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Smith normal form

In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries in a principal ideal domain (PID). The Smith normal form of a matrix is diagonal, and can be obtained from the original matrix by multiplying on the left and right by invertible square matrices. In…

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Definition

Algorithm

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Run-time complexity

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Map overview Semantic statistics

Smith normal form

Nodes49
Edges48
Triples62
Avg. degree1.96
Density0.040816
Components1

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Smith normal form

Top relations

related to References · 25
Smith normal form → Clarendon Press, Example, Glaisher, Henry, Henry John Stephen Smith, JSTOR, Lecture Notes, Linear Algebra, Lond, Matthews, MP274, On, Oxford, Phil, PlanetMath, Queensland, Reprinted, S2CID, Smith, Soc
related to Algorithm · 13
Smith normal form → Bézout, Bézout's, For, In, Once, Only, Phrased, PID, SAT, Since, Smith, The, This
related to External links · 9
Smith normal form → An, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, NumberTheory, Smith, SmithDecomposition, Wikisource-logo, Wolfram Alpha Site
related to Similarity · 5
Smith normal form → For, PID, Smith, Specifically, The Smith
has application · 4
Smith normal form → CW, For, It, The Smith
related to Example · 3
Smith normal form → As, Smith, The
related to Run-time complexity · 3
Smith normal form → If, N-by-N, The Smith Normal Form

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Important terminology

displaystyle matrix smith form normal entries matrices column position diagonal row entry invertible times alpha right pid step example also

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Smith normal formhas applicationThe Smith0.60section
Smith normal formhas applicationFor0.60section
Smith normal formhas applicationCW0.60section
Smith normal formhas applicationIt0.60section
Smith normal formrelated to AlgorithmThe0.60section
Smith normal formrelated to AlgorithmSAT0.60section
Smith normal formrelated to AlgorithmThis0.60section
Smith normal formrelated to AlgorithmOnce0.60section
Smith normal formrelated to AlgorithmSmith0.60section
Smith normal formrelated to AlgorithmPhrased0.60section
Smith normal formrelated to AlgorithmSince0.60section
Smith normal formrelated to AlgorithmOnly0.60section

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