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  2. Distributive property - Wikipedia

    en.wikipedia.org/wiki/Distributive_property

    In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality (+) = + is always true in elementary algebra. For example, in elementary arithmetic , one has 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2 ⋅ 3 ) . {\displaystyle 2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).}

  3. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    2.1 Distributive properties. ... The generalization of the dot product formula to Riemannian manifolds is a defining property of a Riemannian connection, ...

  4. Distributivity (order theory) - Wikipedia

    en.wikipedia.org/wiki/Distributivity_(order_theory)

    The map φ defined by φ(y) = x ∨ y is a lattice homomorphism from L to the upper closure ↑x = { y ∈ L: x ≤ y}; The binary relation Θ x on L defined by y Θ x z if x ∨ y = x ∨ z is a congruence relation, that is, an equivalence relation compatible with ∧ and ∨. [3] In an arbitrary lattice, if x 1 and x 2 are distributive ...

  5. FOIL method - Wikipedia

    en.wikipedia.org/wiki/FOIL_method

    In the second step, the distributive law is used to simplify each of the two terms. Note that this process involves a total of three applications of the distributive property. In contrast to the FOIL method, the method using distributivity can be applied easily to products with more terms such as trinomials and higher.

  6. Cross product - Wikipedia

    en.wikipedia.org/wiki/Cross_product

    [2] The cross product is anticommutative (that is, a × b = − b × a) and is distributive over addition, that is, a × (b + c) = a × b + a × c. [1] The space together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.

  7. GF (2) - Wikipedia

    en.wikipedia.org/wiki/GF(2)

    every element x of GF(2) satisfies x + x = 0 and therefore −x = x; this means that the characteristic of GF(2) is 2; every element x of GF(2) satisfies x 2 = x (i.e. is idempotent with respect to multiplication); this is an instance of Fermat's little theorem. GF(2) is the only field with this property (Proof: if x 2 = x, then either x = 0 or ...

  8. Father of 2 Missing Since the Holidays Reportedly Found Dead ...

    www.aol.com/lifestyle/father-2-missing-since...

    The body of a Michigan father who went missing while attending a family gathering over the holidays has reportedly been found. On Saturday, Jan. 4 at approximately 2 p.m. local time, 52-year-old ...

  9. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    If the scalars have the commutative property, then all four matrices are equal. More generally, all four are equal if c belongs to the center of a ring containing the entries of the matrices, because in this case, cX = Xc for all matrices X. These properties result from the bilinearity of the product of scalars: