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  2. Lists of vector identities - Wikipedia

    en.wikipedia.org/wiki/Lists_of_vector_identities

    Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.

  3. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant. The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:

  4. Vector algebra relations - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra_relations

    The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.

  5. Green's identities - Wikipedia

    en.wikipedia.org/wiki/Green's_identities

    This identity is derived from the divergence theorem applied to the vector field F = ψ ∇φ while using an extension of the product rule that ∇ ⋅ (ψ X) = ∇ψ ⋅X + ψ ∇⋅X: Let φ and ψ be scalar functions defined on some region U ⊂ R d, and suppose that φ is twice continuously differentiable, and ψ is once continuously differentiable.

  6. Lagrange's identity - Wikipedia

    en.wikipedia.org/wiki/Lagrange's_identity

    [5] [6] Since the right-hand side of the identity is clearly non-negative, it implies Cauchy's inequality in the finite-dimensional real coordinate space R n and its complex counterpart C n. Geometrically, the identity asserts that the square of the volume of the parallelepiped spanned by a set of vectors is the Gram determinant of the vectors.

  7. Senate Democrats name top leadership positions after losing ...

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    Senate Democrats held a closed-door election Tuesday morning to name who would fill their top leadership posts for the next two years, most notably filling the No. 3 position held by a retiring ...

  8. Identity (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Identity_(mathematics)

    Visual proof of the Pythagorean identity: for any angle , the point (,) = (⁡, ⁡) lies on the unit circle, which satisfies the equation + =.Thus, ⁡ + ⁡ =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...

  9. October inflation data meets forecasts, keeping Fed on track ...

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    For the month of October, the three-month annualized rate for core CPI rose to 3.6% versus the prior 3.1%. The six-month annualized rate held steady at 3.3%. The Fed's path forward.

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