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Что (кто) такое vector space - определение

Vector space

$Addition of functions: the sum of the sine and the exponential function is <math>\sin+\exp:\R\to\R</math> with <math>(\sin+\exp)(x)=\sin(x)+\exp(x)</math>.$

THE BASIC ALGEBRAIC STRUCTURE OF LINEAR ALGEBRA; A MODULE OVER A FIELD, SUCH THAT ITS ELEMENTS CAN BE ADDED TOGETHER OR SCALED BY ELEMENTS OF THE FIELD

VectorSpaces; Vector Space; Linear space; Vector theory; Vector spaces; Vectorspace; Real vector space; Complex vector space; Coordinate space; Coordinate vector space; Coordinate linear space; Linear coordinate space; Abstract vector space; Complex Vector Spaces; Field of scalars; Complex vector; Real vector; Vectors and Scalars; Vectorial space; Vectorial Space; Linear vector space; Space-vector; Space vector; General vector space; Several variables; Vector line; Vector plane; Vector hyperplane; Applications of vector spaces; Vector space over a field

In mathematics, physics, and engineering, a vector space (also called a linear space) is a set whose elements, often called vectors, may be added together and multiplied ("scaled") by numbers called scalars. Scalars are often real numbers, but can be complex numbers or, more generally, elements of any field.

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

vector space

$Addition of functions: the sum of the sine and the exponential function is <math>\sin+\exp:\R\to\R</math> with <math>(\sin+\exp)(x)=\sin(x)+\exp(x)</math>.$

THE BASIC ALGEBRAIC STRUCTURE OF LINEAR ALGEBRA; A MODULE OVER A FIELD, SUCH THAT ITS ELEMENTS CAN BE ADDED TOGETHER OR SCALED BY ELEMENTS OF THE FIELD

VectorSpaces; Vector Space; Linear space; Vector theory; Vector spaces; Vectorspace; Real vector space; Complex vector space; Coordinate space; Coordinate vector space; Coordinate linear space; Linear coordinate space; Abstract vector space; Complex Vector Spaces; Field of scalars; Complex vector; Real vector; Vectors and Scalars; Vectorial space; Vectorial Space; Linear vector space; Space-vector; Space vector; General vector space; Several variables; Vector line; Vector plane; Vector hyperplane; Applications of vector spaces; Vector space over a field

<mathematics> An additive group on which some (scalar) field has an associative multiplicative action which distributes over the addition of the vector space and respects the addition of the (scalar) field: for vectors u, v and scalars h, k; h(u+v) = hu + hv; (h+k)u = hu + ku; (hk)u = h(ku). [Simple example?] (1996-09-30)

linear space

$Addition of functions: the sum of the sine and the exponential function is <math>\sin+\exp:\R\to\R</math> with <math>(\sin+\exp)(x)=\sin(x)+\exp(x)</math>.$

THE BASIC ALGEBRAIC STRUCTURE OF LINEAR ALGEBRA; A MODULE OVER A FIELD, SUCH THAT ITS ELEMENTS CAN BE ADDED TOGETHER OR SCALED BY ELEMENTS OF THE FIELD

VectorSpaces; Vector Space; Linear space; Vector theory; Vector spaces; Vectorspace; Real vector space; Complex vector space; Coordinate space; Coordinate vector space; Coordinate linear space; Linear coordinate space; Abstract vector space; Complex Vector Spaces; Field of scalars; Complex vector; Real vector; Vectors and Scalars; Vectorial space; Vectorial Space; Linear vector space; Space-vector; Space vector; General vector space; Several variables; Vector line; Vector plane; Vector hyperplane; Applications of vector spaces; Vector space over a field

<mathematics> A vector space where all linear combinations of elements are also elements of the space. This is easy for spaces of numbers but not for a space of functions. Roughly, this is to say that multiplication by numbers, and addition of elements is defined in the space. (2000-03-10)