Understanding Quotient Vector Space: Collapsing to Zero

In summary, the conversation is about quotient spaces of a vector space. The definition of a quotient vector space is discussed, with one person expressing confusion about the concept of "collapsing" a subspace to zero. Another person asks about the zero vector of V/N and the conversation ends with the acknowledgement that further review of the basics is necessary.
  • #1
matheinste
1,068
0
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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  • #2
What's the zero vector of V/N?
 
  • #3
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.
 

1. What is Quotient Vector Space?

Quotient Vector Space is a mathematical concept that deals with the division of a vector space by a subspace. It is a way to create a new vector space by collapsing certain elements of the original space together.

2. What is the purpose of collapsing to zero in Quotient Vector Space?

The purpose of collapsing to zero in Quotient Vector Space is to remove redundant or irrelevant information from the vector space. This allows for a more efficient and simplified representation of the original space.

3. How is Understanding Quotient Vector Space useful in scientific research?

Understanding Quotient Vector Space is useful in scientific research as it provides a way to reduce the complexity of a vector space and focus on the most relevant information. This can help in data analysis, pattern recognition, and classification tasks.

4. Can Quotient Vector Space be applied to real-life problems?

Yes, Quotient Vector Space can be applied to real-life problems. It has applications in various fields such as machine learning, image and signal processing, and information retrieval. It allows for a more efficient representation of data and can aid in solving complex problems.

5. Are there any limitations to using Quotient Vector Space?

Like any mathematical concept, there are limitations to using Quotient Vector Space. It may not be applicable to all types of data and may result in loss of information during the collapsing process. It also requires a certain level of understanding and mathematical knowledge to effectively use it in research.

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