# Unit III: Vector and Vector Space | BCA 2nd Semester Mathematics II Notes Pdf

A vector space, also known as a linear space, is a collection of items called vectors that are put together and multiplied ("scaled") by numbers known as scalars. Scalars are commonly thought of as being real numbers. With vector spaces, however, there are only a few situations of scalar multiplication by rational numbers, complex numbers, and so on. Vector addition and scalar multiplication algorithms must meet specific criteria, such as axioms. Scalars are defined as real or complex numbers using real vector space and complex vector space.

Vector space is a space made up of vectors that are defined by the associative and commutative rule of vector addition, as well as the associative and distributive process of vector multiplication by scalars. A vector space is made up of a set of V (named vectors by its members), a field F (called scalars by its elements), and two operations.

1. Vector addition is an operation that takes two vectors u, v ∈ V, and it produces the third vector u + v ∈ V
2. Scalar Multiplication is an operation that takes a scalar c ∈ F and a vector v ∈ V and it produces a new vector uv ∈ V.

In this “Vector and Vector Space - Mathematics II” you will learn about the following topics:

1. Introduction to vector and vector space
2. Vector space and subspaces with examples
3. Linear combination of vectors
4. Linear
5. Dependence and independence of vectors
6. Basis and dimension of vector space

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This article Vector and Vector Space - Mathematics II - Mathematics II is contributed by Namrata Chaudhary, a student of Lumbini Engineering College (LEC).

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