Understanding Quotient Vector Space: Collapsing to Zero

[matheinste]

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.

 

[morphism]

What's the zero vector of V/N?

 

[matheinste]

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.