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  2. Matrix multiplication - Wikipedia

    en.wikipedia.org/wiki/Matrix_multiplication

    The dot product of two vectors and of equal length is equal to the single entry of the matrix resulting from multiplying these vectors as a row and a column vector, thus: (or , which results in the same matrix).

  3. Hadamard product (matrices) - Wikipedia

    en.wikipedia.org/wiki/Hadamard_product_(matrices)

    The Hadamard product operates on identically shaped matrices and produces a third matrix of the same dimensions. In mathematics, the Hadamard product (also known as the element-wise product, entrywise product [1]: ch. 5 or Schur product [2]) is a binary operation that takes in two matrices of the same dimensions and returns a matrix of the multiplied corresponding elements.

  4. Product (mathematics) - Wikipedia

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

    In mathematics, a product is the result of multiplication, or an expression that identifies objects (numbers or variables) to be multiplied, called factors.For example, 21 is the product of 3 and 7 (the result of multiplication), and (+) is the product of and (+) (indicating that the two factors should be multiplied together).

  5. Product measure - Wikipedia

    en.wikipedia.org/wiki/Product_measure

    Then, for the minimal product measure the measure of a set is the sum of the measures of its horizontal sections, while for the maximal product measure a set has measure infinity unless it is contained in the union of a countable number of sets of the form A×B, where either A has Lebesgue measure 0 or B is a single point. (In this case the ...

  6. Cross product - Wikipedia

    en.wikipedia.org/wiki/Cross_product

    The cross product with respect to a right-handed coordinate system. In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .

  7. Frobenius inner product - Wikipedia

    en.wikipedia.org/wiki/Frobenius_inner_product

    In mathematics, the Frobenius inner product is a binary operation that takes two matrices and returns a scalar.It is often denoted , .The operation is a component-wise inner product of two matrices as though they are vectors, and satisfies the axioms for an inner product.

  8. Semidirect product - Wikipedia

    en.wikipedia.org/wiki/Semidirect_product

    The direct product of two groups N and H can be thought of as the semidirect product of N and H with respect to φ(h) = id N for all h in H. Note that in a direct product, the order of the factors is not important, since N × H is isomorphic to H × N. This is not the case for semidirect products, as the two factors play different roles.

  9. Seven-dimensional cross product - Wikipedia

    en.wikipedia.org/.../Seven-dimensional_cross_product

    The restriction to 0, 1, 3 and 7 dimensions is related to Hurwitz's theorem, that normed division algebras are only possible in 1, 2, 4 and 8 dimensions. The cross product is formed from the product of the normed division algebra by restricting it to the 0, 1, 3, or 7 imaginary dimensions of the algebra, giving nonzero products in only three ...

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