Subspaces
A subset W of a vector space V is called a subspace of V if W is itself a vector space under the addition and scalar multiplication defined on V.
Subspaces are subsets of a vector space that themselves form vector spaces. Operations of vector addition and scalar multiplication from the larger vector space are applicable to vector space. Subspaces satisfies all axion/properties of vector space.
- Contain the zero vector
- Is closed under addition
- Is closed under scalar multiplication
They can be lower-dimensional spaces within the larger vector space and can provide insights into the structure and properties of the vector space as a whole.
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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