Hurwitz's theorem (composition algebras)
In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form. The theorem states that if the quadratic form defines a homomorphism into the positive real numbers on the non-zero part of the algebra, then the algebra must be isomorphic to the real numbers, the complex numbers, the quaternions or the octonions. Such algebras, sometimes called Hurwitz algebras, are examples of composition algebras.
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Hurwitz's theorem (composition algebras)
In mathematics, Hurwitz's theorem is a theorem of Adolf Hurwitz (1859–1919), published posthumously in 1923, solving the Hurwitz problem for finite-dimensional unital real non-associative algebras endowed with a positive-definite quadratic form. The theorem states that if the quadratic form defines a homomorphism into the positive real numbers on the non-zero part of the algebra, then the algebra must be isomorphic to the real numbers, the complex numbers, the quaternions or the octonions. Such algebras, sometimes called Hurwitz algebras, are examples of composition algebras.
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En mathématiques, diverses ver ...... uaternions) et 𝕆 (octonions).
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In mathematics, Hurwitz's theo ...... ion of simple Jordan algebras.
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Теорема Гурвица о нормированны ...... матиком Гурвицем в 1898 году..
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在代数学中,胡尔维兹定理(又名“1,2,4,8定理”)是以在 ...... 个平方和的积仍可以写成n个平方和仅当n为1,2,4或者8时。
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En mathématiques, diverses ver ...... uaternions) et 𝕆 (octonions).
@fr
In mathematics, Hurwitz's theo ...... mples of composition algebras.
@en
Теорема Гурвица о нормированны ...... матиком Гурвицем в 1898 году..
@ru
在代数学中,胡尔维兹定理(又名“1,2,4,8定理”)是以在 ...... 个平方和的积仍可以写成n个平方和仅当n为1,2,4或者8时。
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Hurwitz's theorem (composition algebras)
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Théorème de Frobenius généralisé
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Теорема Гурвица о нормированных алгебрах с делением
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胡尔维兹定理
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