What do you understand by the term vector space?

While the set of vectors V as well as the two operations are to be explicitly defined, the set of real numbers is assumed to be set of scalars unless stated otherwise. . In Linear Algebra, the idea of vectors start with a set of ordered n-tuples This set is called n-space as well as is represented by Rn We are familiar with R2 (Cartesian Plane) as well as R3 (Cartesian three dimensional space) which correspondingly consist of set of all ordered pairs as well as ordered triples. It can be analyzed that the common arithmetical operations of additions as well as scalar multiplications as well as their properties can be extended to the general n-space Rn Similarly that, addition as well as scalar multiplication can be conveniently defined for other Mathematical objects like, Matrices, functions, Polynomials as well as Integrals. These operations can be defined in such a manner, that they share the same properties of common addition as well as scalar multiplication available for Rn The properties of addition as well as scalar multiplication are abstracted as axioms to define the notion of Vector Space . .

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