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Homework Help: Quick one about notation.

  1. Dec 6, 2014 #1
    1. The problem statement, all variables and given/known data
    How to indicate that a vector b is in the span of the columns of a matrix C?

    2. Relevant equations
    I could type the definition of Span here, but Wikipedia has it too and it is not necessary or useful now.

    3. The attempt at a solution
    [tex] \mathbf{b} \in \mathrm{Span}\{\mathbf{c}_1, \mathbf{c}_2, \ldots, \mathbf{c}_n\} [/tex]

    I've never seen the [itex]\in[/itex] symbol in this context and wanted to be sure it is OK. As the concept of span seems to be defined formally in such a way that it ends up being a set, I think this operator is the right one.
  2. jcsd
  3. Dec 6, 2014 #2


    Staff: Mentor

    The above represents a set of vectors, and ##\in## simply means that b belongs to that set.
  4. Dec 6, 2014 #3
    This is a yes, right? (slow guy)
  5. Dec 6, 2014 #4


    Staff: Mentor


    BTW, the span of a set of vectors is a set, albeit an infinite set - the set of all linear combinations of the vectors listed in the set.
  6. Dec 6, 2014 #5
    What about [tex]\mathrm{Span}\{\varnothing\}[/tex]?
  7. Dec 7, 2014 #6


    Staff: Mentor

    I've never seen this, but I would guess that it's the empty set.
  8. Dec 8, 2014 #7


    User Avatar
    Science Advisor

    Mark44 should have said "the span of any non-empty set of vectors is infinite".
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