Understanding Quotient Vector Space: Collapsing to Zero

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SUMMARY

The discussion centers on the concept of Quotient Vector Space, specifically the process of collapsing a subspace N to zero within a vector space V. The zero vector of the quotient space V/N is defined as 0 + N, where 0 is the zero vector of V. Participants emphasize the importance of understanding the foundational principles of vector spaces and their subspaces to grasp the concept of quotient spaces fully.

PREREQUISITES
  • Understanding of vector spaces and subspaces
  • Familiarity with the concept of equivalence classes in mathematics
  • Basic knowledge of linear algebra
  • Comprehension of the zero vector and its properties
NEXT STEPS
  • Study the properties of vector spaces and subspaces in linear algebra
  • Learn about equivalence relations and classes in mathematical contexts
  • Explore examples of Quotient Vector Spaces in linear algebra
  • Investigate applications of quotient spaces in advanced mathematics
USEFUL FOR

Students and educators in mathematics, particularly those studying linear algebra, as well as anyone seeking to deepen their understanding of vector spaces and quotient structures.

matheinste
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Hello all

I have read about quotient spaces of a vector space in several books and have an understanding of what they are.

Looking up Quotient Vector Space in Wiki it says :-

The quotient of a vector space V by a subspace N is a vector space obtained by "collapsing" N to zero.

I don't understand the collapsing to zero bit.

Thanks for any help Matheinste.
 
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What's the zero vector of V/N?
 
Thanks for your reply.

As [x]=x+n where n is in N i suppose the zero vector is 0+N but my lack of confidence shows that i don't really understand as much as i thought and so must go back to basics.

Matheinste.
 

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