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  2. Scalar multiplication - Wikipedia

    en.wikipedia.org/wiki/Scalar_multiplication

    Scalar multiplication of a vector by a factor of 3 stretches the vector out. The scalar multiplications −a and 2a of a vector a. In mathematics, scalar multiplication is one of the basic operations defining a vector space in linear algebra [1] [2] [3] (or more generally, a module in abstract algebra [4] [5]).

  3. Vector multiplication - Wikipedia

    en.wikipedia.org/wiki/Vector_multiplication

    In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the ...

  4. Scalar (mathematics) - Wikipedia

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

    A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.

  5. Vector-valued function - Wikipedia

    en.wikipedia.org/wiki/Vector-valued_function

    A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...

  6. Vector calculus identities - Wikipedia

    en.wikipedia.org/wiki/Vector_calculus_identities

    Another method of deriving vector and tensor derivative identities is to replace all occurrences of a vector in an algebraic identity by the del operator, provided that no variable occurs both inside and outside the scope of an operator or both inside the scope of one operator in a term and outside the scope of another operator in the same term ...

  7. Vector space - Wikipedia

    en.wikipedia.org/wiki/Vector_space

    Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2 w . In mathematics and physics , a vector space (also called a linear space ) is a set whose elements, often called vectors , can be added together and multiplied ...

  8. Complex conjugate of a vector space - Wikipedia

    en.wikipedia.org/wiki/Complex_conjugate_of_a...

    In other words, the scalar multiplication of ¯ satisfies = ¯ where is the scalar multiplication of ¯ and is the scalar multiplication of . The letter v {\displaystyle v} stands for a vector in V , {\displaystyle V,} α {\displaystyle \alpha } is a complex number, and α ¯ {\displaystyle {\overline {\alpha }}} denotes the complex conjugate ...

  9. Vector (mathematics and physics) - Wikipedia

    en.wikipedia.org/wiki/Vector_(mathematics_and...

    Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w . In mathematics and physics , a vector space (also called a linear space) is a set whose elements, often called vectors , can be added together and multiplied ...