Vector Space
What is a Vector Space?
A vector space is a mathematical structure that consists of a set of vectors, along with operations of addition and scalar multiplication that satisfy specific properties.
What are Properties of a Vector Space?
Properties of a vector space include closure under addition and scalar multiplication, associativity and commutativity of addition, existence of additive identity (zero vector), existence of additive inverses, compatibility of scalar multiplication with field multiplication, and distributivity of scalar multiplication over vector addition.
What is Difference between a Vector Space and a Subspace?
A vector space is a set of vectors with defined addition and scalar multiplication operations that satisfy certain properties. A subspace is a subset of a vector space that is itself a vector space under the same operations.
What is Dimension of a Vector Space?
Dimension of a vector space is the number of vectors in any basis for that vector space. It is a measure of the space’s “size” or complexity.
What are Examples of Vector Spaces?
Some examples of vector space includes, Polynomial Space, Function Spaces, Matrix Space, Complex Vector Space, etc.
What are Equal Vectors?
Vector that have equal magnitude and and same direction are called Equal Vectors.
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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