1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Subspace, Linear Algebra, C^n[a,b]

  1. Feb 25, 2010 #1
    Show that C^n[a,b] is a subspace of C[a,b] where C^n is the nth derivative.

    I know the set is non empty since f(x)=x exist; however, I don't know how to start either the multiplication or addition property of subspaces to confirm that C^n is a subspace.

    Thanks ahead of time for any help any of you may have.
  2. jcsd
  3. Feb 25, 2010 #2
    What's the derivative of the sum of two functions? What's the derivative of a function multiplied by a constant?
  4. Feb 25, 2010 #3

    That works for generalization all nth derivative functions?
  5. Feb 25, 2010 #4
    Your expressions don't make much sense. If I'm reading them right (and please, try to use Latex), you're saying that:

    [tex]\left(\alpha f\left(x\right)\right)^{n}=n\alpha\left(\alpha f\left(x\right)\right)^{n-1}[/tex]

    That doesn't make much sense.
  6. Feb 25, 2010 #5
    multiplication: [tex]\alpha[/tex]*n*[tex]f^{n-1}(x)[/tex]
    addition: n*[tex](f+g)^{n-1}[/tex] = n*[[tex]f^{n-1}(x)[/tex]+[tex]g^{n-1}(x)[/tex]]
    and then the n distributes.

    Does this generalize all nth derivatives?

    Is there away for me to import from Maple since I have Maple and Latex is to slow and cumbersome?
  7. Feb 25, 2010 #6
    Those expressions are wrong, given functions f,g and a constant c, their n-th derivatives are:



  8. Feb 25, 2010 #7
    But when the derivative is taking, don't the functions need to be multiplied by n and then the derivative is n-1?
  9. Feb 25, 2010 #8
    You are confusing the derivative of a power with the n-th derivative.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Threads - Subspace Linear Algebra Date
Subsets in R^3 Jan 16, 2018
Linear Algebra subspace help Dec 30, 2017
Verifying subspaces Jan 28, 2017
A real parameter guaranteeing subspace invariance Nov 4, 2016
Subspace question May 9, 2016