Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Span(S1 ∩ S2) ⊆ span(S1) ∩ span(S2)

  1. Jun 8, 2009 #1
    Hi! I wonder if you guys help me prove this:
    span(S1 ∩ S2) ⊆ span(S1) ∩ span(S2)
    I have seen span(S1 U S2) = span(S1) + span(S2), so I just want to prove this one, any suggestion?
     
  2. jcsd
  3. Jun 8, 2009 #2

    MathematicalPhysicist

    User Avatar
    Gold Member

    v=as, s in S1 and S2, thus v is in sp(S1) and sp(S2).
    Vice versa isn't necessarily because if v in sp(S1) and sp(S2), then v=as1=bs2, and s1 isn't necessarily in S2 and s2 isn't necessarily in S1.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Span(S1 ∩ S2) ⊆ span(S1) ∩ span(S2)
  1. Reading Span (Replies: 1)

  2. Vectors and spanning (Replies: 6)

  3. Span of Vectors (Replies: 2)

  4. Span of functions (Replies: 3)

  5. Span of Vectors (Replies: 3)

Loading...