DefinitionComplex vector space:- A vector space is defined over the field of complex numbers, collection of all the possible vectors is called a vector space, however, it also satisfies properties such as closer: a + b ε R, associativity:. Also it may be noted that these vector spaces are extension of vector spaces over real numbers and lead to a framework to study geometric structures and transformations in complex vector fields so. Therefore it necessary to have its properties and characteristics in detail. They are used in another field of study, quantum mechanics, electromagnetism, functional analysis to simulate physical quantities and complex systems. Illustration:- Let, f X = u x + iv x = A function which satisfies the above property where u, v are real-valued function of a real variable x.Then, it can be said that the above function is a vector space over scalars x in R with standard operations of pointwise addition and scalar multiplication.
