Please explain the general relationship between abstract
algebra and linear algebra.
Also, please...

Question

Please explain the general relationship between abstract 
algebra and linear algebra.
Also, please dscuss how it is possible to considerably shorten 
the list of properties that define a vector space by using definitions from 
abstract algebra. This needs toinclude an explicit list of the properties of a vector space that are still 
needed after applying the concept of abelian group.

David · Accepted Answer

Question: - Please explain the general relationship between abstract algebra and 
linear algebra. Also, please discuss how it is possible to considerably shorten 
the list of properties that define a vector space by using definitions from 
abstract algebra. This needs to include an explicit list of the properties of a 
vector space that are still needed after applying the concept of Abelian group.
Solution:-  
First of all let us understand the definition of both Abstract algebra and Linear 
Algebra.
Definition of Abstract Algebra:-  
It is defined as the study of algebraic structure such as groups, rings, fields, vector spaces etc.  and 
their properties. 
Definition of Linear Algebra:- 
It is the branch of mathematics concerning vector spaces, often finite or countably 
infinite dimensional, as well as linear mappings between such spaces. 
 
Abstract Algebra can be considered as component of linear algebra in the sense that the sets that linear 
algebra is built around (Abelian groups) are a backbone of Abstract Algebra.  In some of the books, it 
seems that Abstract Algebra always start with Groups and continues through Rings and Fields.  In some 
other books,

Please explain the general relationship between abstract algebra and linear algebra. Also, please dscuss how it is possible to considerably shorten the list of properties that define a vector space by...

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