What is Vector Space?
A space in mathematics comprised of vectors, that follow the associative and commutative law of addition of vectors and the associative and distributive process of multiplication of vectors by scalars is called vector space. In vector space, it consists of a set of V (elements of V are called vectors), a field F (elements of F are scalars) and the two arithmetic operations
Vector Addition: It is an operation that takes two vectors u, v ∈ V, and it produces the third vector u + v ∈ V
Scalar Multiplication: It is an operation that takes a scalar c ∈ F and a vector v ∈ V and produces a new vector uv ∈ V.
Vector Space Definition
A space comprised of vectors, collectively with the associative and commutative law of addition of vectors and also the associative and distributive process of multiplication of vectors by scalars is called vector space.
- Vector Addition is an operation that takes two vectors u, v ∈ V, and it produces the third vector u + v ∈ V
- Scalar Multiplication is an operation that takes a scalar c ∈ F and a vector v ∈ V and it produces a new vector uv ∈ V
Vector Space- Definition, Axioms, Properties and Examples
A vector space is a group of objects called vectors, added collectively and multiplied by numbers, called scalars. Scalars are usually considered to be real numbers. But there are few cases of scalar multiplication by rational numbers, complex numbers, etc. with vector spaces.
In this article, we have covered Vector Space Definition, Axions, Properties and others in detail.
Table of Content
- What is Vector Space?
- Vector Space Axioms
- Vector Space Examples
- Dimension of a Vector Space
- Vector Addition and Scalar Multiplication
- Vector Space Properties
- Subspaces
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