Scalars and determining subspaces

  • Thread starter MoreDrinks
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  • #1
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To determine if a subset of a vector space is a subspace, it must be closed under addition and scalar multiplication. As far as I can tell, this means adding two arbitrary vectors in the subset and having the sum be within the subset.

But...can the scalar be any number? Is there any limitation?
 

Answers and Replies

  • #2
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If ##W## is a subspace of ##V##, then ##\alpha v\in W## for any scalar ##\alpha## and for any ##w\in W##.
 
  • #3
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If ##W## is a subspace of ##V##, then ##\alpha v\in W## for any scalar ##\alpha## and for any ##w\in W##.
Thanks, my book is terrible.
 

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