scalar (mathematics) wikipedia - EAS

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  1. Scalar (mathematics) From Wikipedia, the free encyclopedia A scalar is an element of a field which is used to define a vector space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector.
    en.wikipedia.org/wiki/Scalar_(mathematics)
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    What is a scalar in math?
    A scalar is an element of a field which is used to define a vector space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector. In linear algebra, real numbers or other elements of a field are called scalars and relate to vectors in a vector space through...
    en.wikipedia.org/wiki/Scalar_(mathematics)
    What is scalar multiplication in linear algebra?
    In linear algebra, real numbers or other elements of a field are called scalars and relate to vectors in a vector space through the operation of scalar multiplication, in which a vector can be multiplied by a number to produce another vector.
    en.wikipedia.org/wiki/Scalar_(mathematics)
    What are the scalars of vector spaces?
    Scalars of vector spaces. For example, in a coordinate space, the scalar multiplication yields . In a (linear) function space, kƒ is the function x ↦ k ( ƒ ( x )). The scalars can be taken from any field, including the rational, algebraic, real, and complex numbers, as well as finite fields .
    en.wikipedia.org/wiki/Scalar_(mathematics)
    What is an example of scalar transformation in math?
    Another example comes from manifold theory, where the space of sections of the tangent bundle forms a module over the algebra of real functions on the manifold. The scalar multiplication of vector spaces and modules is a special case of scaling, a kind of linear transformation .
    en.wikipedia.org/wiki/Scalar_(mathematics)
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    Scalar (mathematics) - Wikipedia

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

    A scalar is an element of a field which is used to define a vector space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a vector. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated

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    The word scalar derives from the Latin word scalaris, an adjectival form of scala (Latin for "ladder"), from which the English word scale also comes. The first recorded usage of the word "scalar" in mathematics occurs in

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    Scalars of vector spaces
    A vector space is defined as a set of vectors (additive abelian group), a set of scalars (field), and a scalar multiplication operation that takes a scalar k and a vector v to another vector kv. For example, in a

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  4. Scalar - Simple English Wikipedia, the free encyclopedia

    https://simple.wikipedia.org/wiki/Scalar

    In mathematics, scalars are distinguished from more complex mathematical objects such as vectors and matrices in that they consist of only one number. A scalar k {\displaystyle k} can also be multiplied to a vector v {\displaystyle \mathbf {v} } or a matrix A {\displaystyle A} , resulting in the vector k v {\displaystyle k\mathbf {v} } and the ...

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    • Scalar - Wikipedia

      https://en.wikipedia.org/wiki/Scalar

      Scalar may refer to:
      • Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers
      • Scalar (physics), a physical quantity that can be described by a single element of a number field such as a real number

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    • Scalar - Encyclopedia of Mathematics

      https://encyclopediaofmath.org/wiki/Scalar

      The term "scalar" comes from the original meaning as a quantity which can be completely specified by one (real) number. A scalar field on a manifold $ M $ is a function on $ M $; that is, a scalar field, or field of scalars, is a tensor field (cf. Tensor bundle) of rank $ ( 0, 0) $. These are the scalars in the algebra of tensor fields on $ M ...

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