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Span of functions

  1. Sep 24, 2014 #1
    So let's say I have a function that I want to find out if is in the span of two other functions, for example, a*f + b*g = h, where f, g, and h are functions, and a and b are constants. Let's say I find a solution where a and b are not constants. Does that still mean that h is in the span of f and g, even though a and b are not constants?
     
  2. jcsd
  3. Sep 24, 2014 #2

    FactChecker

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    No
     
  4. Sep 24, 2014 #3

    Mark44

    Staff: Mentor

    For a function h to be in the span of two other functions f and g, h must be a linear combination of f and g. IOW, h = af + bg, where a and b are constants. It's almost exactly the same definition for a vector to be in the span of two other vectors.
     
  5. Sep 24, 2014 #4

    Bacle2

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    It would be nice if the OP could be more specific about the vector space s/he is working in; gummz, can
    you tell us more about what space you are working in? are g,h part of a basis for the space?
     
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