Subspace and subset

  • Thread starter Max.Planck
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  • #1
Max.Planck
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Hi,

A quick question:
Does a set need to be a subset to be a subspace of some vector space?
 

Answers and Replies

  • #2
micromass
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Hi,

A quick question:
Does a set need to be a subset to be a subspace of some vector space?

Yes, a subspace of a vector space V necessarily needs to be a subset.
 
  • #3
HallsofIvy
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A vector space is a set of objects with "addition" and "scalar multiplication" defined. A "subspace" is a subset with the "inherited" addition and scalar multiplication.
 
  • #4
Max.Planck
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A vector space is a set of objects with "addition" and "scalar multiplication" defined. A "subspace" is a subset with the "inherited" addition and scalar multiplication.

Thank you!
 

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