Difference Between Vector Space and Euclidean Space
Vector Space |
Euclidean Space |
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Vector space is an abstract algebraic structure defined by vector addition and scalar multiplication |
Euclidean space is a geometric space characterized by distances and coordinates. |
Vector space focuses on the algebraic properties of vectors and their operations |
Euclidean space focuses on the geometric properties of points, lines, distances, and angles within a specific coordinate system. |
Vector spaces are used in linear algebra and various mathematical theories. |
Euclidean spaces are used extensively in geometry, physics, engineering, and other fields where spatial relationships and measurements are important |
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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