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 particular, the integers are a PID, so one can always calculate the Smith normal form of an integer matrix. The Smith normal form is very useful for working with finitely generated modules over a PID, and in particular for deducing the structure of a quotient of a free module. It is named after the British mathematician Henry John Stephen Smith.
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Abelian groupArrangement of hyperplanesCanonical formChinese remainder theoremComputational complexity of matrix multiplicationComputational topologyDiophantine equationElimination theoryFermat (computer algebra system)Finitely generated abelian groupFree abelian groupFrobenius normal formHenry John Stephen SmithHermite normal formHomology (mathematics)Invariant factorLinear equation over a ringMatrix equivalenceMatrix similarityModule homomorphismSNFSchmidt Normal FormSchmidt normal formStructure theorem for finitely generated modules over a principal ideal domainSystem of bilinear equations
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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 particular, the integers are a PID, so one can always calculate the Smith normal form of an integer matrix. The Smith normal form is very useful for working with finitely generated modules over a PID, and in particular for deducing the structure of a quotient of a free module. It is named after the British mathematician Henry John Stephen Smith.
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Die Smith-Normalform ist in de ...... ry John Stephen Smith benannt.
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En matemàtiques, la forma norm ...... ohn Stephen Smith (1826-1883).
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In mathematics, the Smith norm ...... cian Henry John Stephen Smith.
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Нормальна форма Сміта — це діа ...... і справа на оборотні матриці.
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Нормальная форма Смита — это д ...... и справа на обратимые матрицы.
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title
Example of Smith normal form
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Smith normal form
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urlname
ExampleOfSmithNormalForm
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GausssAlgorithmForPrincipalIdealDomains
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Die Smith-Normalform ist in de ...... ry John Stephen Smith benannt.
@de
En matemàtiques, la forma norm ...... ohn Stephen Smith (1826-1883).
@ca
In mathematics, the Smith norm ...... cian Henry John Stephen Smith.
@en
Нормальна форма Сміта — це діа ...... і справа на оборотні матриці.
@uk
Нормальная форма Смита — это д ...... и справа на обратимые матрицы.
@ru
label
Forma normal de Smith
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Smith normal form
@en
Smith-Normalform
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Нормальна форма Сміта
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Нормальная форма Смита
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