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  2. Classical Hamiltonian quaternions - Wikipedia

    en.wikipedia.org/wiki/Classical_Hamiltonian...

    Hamilton defined addition of vectors in geometric terms, by placing the origin of the second vector at the end of the first. [9] He went on to define vector subtraction. By adding a vector to itself multiple times, he defined multiplication of a vector by an integer , then extended this to division by an integer, and multiplication (and ...

  3. Minkowski addition - Wikipedia

    en.wikipedia.org/wiki/Minkowski_addition

    For Minkowski addition, the zero set, {}, containing only the zero vector, 0, is an identity element: for every subset S of a vector space, S + { 0 } = S . {\displaystyle S+\{0\}=S.} The empty set is important in Minkowski addition, because the empty set annihilates every other subset: for every subset S of a vector space, its sum with the ...

  4. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    Subtraction of two vectors can be geometrically illustrated as follows: to subtract b from a, place the tails of a and b at the same point, and then draw an arrow from the head of b to the head of a. This new arrow represents the vector (-b) + a, with (-b) being the opposite of b, see drawing. And (-b) + a = a − b. The subtraction of two ...

  5. Addition - Wikipedia

    en.wikipedia.org/wiki/Addition

    Subtraction is itself a sort of inverse to addition, in that adding x and subtracting x are inverse functions. Given a set with an addition operation, one cannot always define a corresponding subtraction operation on that set; the set of natural numbers is a simple example.

  6. Matrix addition - Wikipedia

    en.wikipedia.org/wiki/Matrix_addition

    In mathematics, matrix addition is the operation of adding two matrices by adding the corresponding entries together. For a vector , v → {\displaystyle {\vec {v}}\!} , adding two matrices would have the geometric effect of applying each matrix transformation separately onto v → {\displaystyle {\vec {v}}\!} , then adding the transformed vectors.

  7. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    Using the algebraic properties of subtraction and division, along with scalar multiplication, it is also possible to “subtract” two vectors and “divide” a vector by a scalar. Vector subtraction is performed by adding the scalar multiple of −1 with the second vector operand to the first vector operand. This can be represented by the ...