Can someone help me with this proof?

  • Thread starter bodensee9
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  • #1
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Homework Statement



Can someone help me with this proof? I'm supposed to show that if a subspace S is contained in subspace V, then S perp contains V perp.

Homework Equations



None, or the dimensions must add up, so S + S perp = some dimension N, and V + V perp equals the same dimension N, if S and V are both subspaces of N.

The Attempt at a Solution



Am I supposed to show that the dimensions don't add up? Can anyone provide suggestions? Thanks.
 

Answers and Replies

  • #2
AKG
Science Advisor
Homework Helper
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S perp contains V perp iff x in V perp implies x in S perp.
x in V perp iff for all y in V, <x,y> = 0.
x in S perp iff for all y in S, <x,y> = 0.

So you want to show (for all y in V, <x,y> = 0) implies (for all y in S, <x,y> = 0). Well S is a subset of V, so this is obvious.
 

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