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  2. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    The length of a vector is defined as the square root of the dot product of the vector by itself, and the cosine of the (non oriented) angle between two vectors of length one is defined as their dot product. So the equivalence of the two definitions of the dot product is a part of the equivalence of the classical and the modern formulations of ...

  3. Geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Geometric_algebra

    In a geometric algebra for which the square of any nonzero vector is positive, the inner product of two vectors can be identified with the dot product of standard vector algebra. The exterior product of two vectors can be identified with the signed area enclosed by a parallelogram the sides of which are the vectors.

  4. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    The generalization of the dot product formula to Riemannian manifolds is a defining property of a Riemannian connection, which differentiates a vector field to give a vector-valued 1-form. Cross product rule

  5. Table of mathematical symbols by introduction date - Wikipedia

    en.wikipedia.org/wiki/Table_of_mathematical...

    unstrict inequality signs (less-than or equals to sign and greater-than or equals to sign) 1670 (with the horizontal bar over the inequality sign, rather than below it) John Wallis: 1734 (with double horizontal bar below the inequality sign) Pierre Bouguer

  6. Trace (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Trace_(linear_algebra)

    If one views any real m × n matrix as a vector of length mn (an operation called vectorization) then the above operation on A and B coincides with the standard dot product. According to the above expression, tr(A ⊤ A) is a sum of squares and hence is nonnegative, equal to zero if and only if A is zero.

  7. 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.

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  9. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    3. Between two groups, may mean that the second one is a proper subgroup of the first one. ≤ 1. Means "less than or equal to". That is, whatever A and B are, A ≤ B is equivalent to A < B or A = B. 2. Between two groups, may mean that the first one is a subgroup of the second one. ≥ 1. Means "greater than or equal to".