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In mathematics, the Grothendieck inequality states that there is a universal constant with the following property. If Mij is an n × n (real or complex) matrix with for all (real or complex) numbers si, tj of absolute value at most 1, then The Grothendieck inequality and Grothendieck constants are named after Alexander Grothendieck, who proved the existence of the constants in a paper published in 1953.

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  • Grothendieck inequality (en)
  • 格羅滕迪克不等式 (zh)
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  • 格羅滕迪克不等式又稱為安蘇納姆梅·蘿狄絲不等式，是數學中表示兩個量 及 , 的關係的不等式，其中是一個希爾伯特空間中的單位球。適合不等式 的最佳常數稱為希爾伯特空間的格羅滕迪克常數。 證明有一個獨立於的上界：定義 格羅滕迪克證明了 之後克里維納（Krivine）證出 即使對此繼續有研究，到現在還不知道確實數值。 (zh)
  • In mathematics, the Grothendieck inequality states that there is a universal constant with the following property. If Mij is an n × n (real or complex) matrix with for all (real or complex) numbers si, tj of absolute value at most 1, then The Grothendieck inequality and Grothendieck constants are named after Alexander Grothendieck, who proved the existence of the constants in a paper published in 1953. (en)
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  • Grothendieck's Constant (en)
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  • GrothendiecksConstant (en)
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  • In mathematics, the Grothendieck inequality states that there is a universal constant with the following property. If Mij is an n × n (real or complex) matrix with for all (real or complex) numbers si, tj of absolute value at most 1, then for all vectors Si, Tj in the unit ball B(H) of a (real or complex) Hilbert space H, the constant being independent of n. For a fixed Hilbert space of dimension d, the smallest constant that satisfies this property for all n × n matrices is called a Grothendieck constant and denoted . In fact, there are two Grothendieck constants, and , depending on whether one works with real or complex numbers, respectively. The Grothendieck inequality and Grothendieck constants are named after Alexander Grothendieck, who proved the existence of the constants in a paper published in 1953. (en)
  • 格羅滕迪克不等式又稱為安蘇納姆梅·蘿狄絲不等式，是數學中表示兩個量 及 , 的關係的不等式，其中是一個希爾伯特空間中的單位球。適合不等式 的最佳常數稱為希爾伯特空間的格羅滕迪克常數。 證明有一個獨立於的上界：定義 格羅滕迪克證明了 之後克里維納（Krivine）證出 即使對此繼續有研究，到現在還不知道確實數值。 (zh)
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