“EulerFoursquareIdentity”的概念、定义、习题解题方法及翻译-数学辞典

单词	EulerFoursquareIdentity
释义	Euler four-square identity The Euler four-square identity simply states that $(x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2})(y_{1}^{2}+y_{2}^{2}+y_{3}^{2}+y_{4}^%{2})=$ $(x_{1}y_{1}+x_{2}y_{2}+x_{3}y_{3}+x_{4}y_{4})^{2}+(x_{1}y_{2}-x_{2}y_{1}+x_{3}%y_{4}-x_{4}y_{3})^{2}$ $+(x_{1}y_{3}-x_{3}y_{1}+x_{4}y_{2}-x_{2}y_{4})^{2}+(x_{1}y_{4}-x_{4}y_{1}+x_{2%}y_{3}-x_{3}y_{2})^{2}$ It may be derived from the property of quaternions that the norm of the product is equal to the product of the norms.
随便看	proof of theorem on equivalent valuations ProofOfTheoremsInAdditivelyIndecomposable proof of theorems in additively indecomposable ProofOfThePowerRule proof of the power rule ProofOfTheRingOfIntegersOfANumberFieldIsFinitelyGeneratedOvermathbbZ proof of the ring of integers of a number field is finitely generated over ℤ ProofOfTheUniformizationTheorem proof of the uniformization theorem ProofOfTheWeakNullstellensatz proof of the weak Nullstellensatz ProofOfTheWellfoundedInductionPrinciple proof of the well-founded induction principle ProofOfThirdIsomorphismTheorem proof of third isomorphism theorem ProofOfThuesLemma proof of Thue’s Lemma ProofOfTietzeExtensionTheorem proof of Tietze extension theorem ProofOfTopologicallyIrreducibleRepresentationsAreAlgebraicallyIrreducibleForCalgebras proof of topologically irreducible representations are algebraically irreducible for C^*-algebras ProofOfTranscendentalRootTheorem proof of transcendental root theorem ProofOfTriangleIncenter proof of triangle incenter

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Euler four-square identity