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November 8th, 2012, 05:44 AM   #1
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direct image inverse image

Show that the subset X of polynominals in R2n[X] all of whose odd coefficients a2i+1 are zero forms a subspace of R2n[X]. Describe D-->(X) and D<--(X).
I need some help with the bolded part.
Thanks in advance!
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November 9th, 2012, 04:02 PM   #2
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Re: direct image inverse image

What is "D"?
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November 10th, 2012, 08:04 AM   #3
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Re: direct image inverse image

differentiation map D
direct image: D-->(x)
inverse image: XD<--(x)
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November 14th, 2012, 02:23 PM   #4
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Re: direct image inverse image

Okay, suppose p(x)= x^4- 3x^2+ 2 (coefficients of all odd powers are 0), then Dp= 4x^3- 6x. What can you say about the derivative of a polynomial with only even powers?
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November 22nd, 2012, 07:35 AM   #5
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Re: direct image inverse image

Thank you...
That is a set of polynomials whose even coefficients are zero, but that is D<--(X). What about the inverse image?
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