Recent content by jpcjr

  1. J

    A LinAlg Proof Involving Orthogonal Complement

    Thank you! By the skin of my teeth, some help from you, and the grace of God, I received the best grade I could have expected in Linear Algebra. Thanks, again! Joe
  2. J

    I need an authoritative answer

    Thank you! By the skin of my teeth, some help from you, and the grace of God, I received the best grade I could have expected in Linear Algebra. Thanks, again! Joe
  3. J

    Prove dual space has the direct sum decomposition

    Thank you! By the skin of my teeth, some help from you, and the grace of God, I received the best grade I could have expected in Linear Algebra. Thanks, again! Joe
  4. J

    What is meant by can be identified with

    Thank you! By the skin of my teeth, some help from you, and the grace of God, I received the best grade I could have expected in Linear Algebra. Thanks, again! Joe
  5. J

    A LinAlg Proof Involving Orthogonal Complement

    Homework Statement Here is the problem and my complete answer. Am I OK? Thanks! http://www.d-series.org/forums/members/52170-albums1546-picture8143.jpg Homework Equations The Attempt at a Solution
  6. J

    I need an authoritative answer

    Thank you very much, as well!
  7. J

    I need an authoritative answer

    Thank you very much!
  8. J

    I need an authoritative answer

    Thank you! Thank you! Thank you! Thank you!
  9. J

    I need an authoritative answer

    I thought the definition of a field was the set of all real numbers plus addition and multiplication (or whatever the particular set of operations are) and since its elements have no direction, by definition, they are not vectors; thus cannot be a vector space. (1) Am I wrong? (2) Can a...
  10. J

    What is meant by can be identified with

    What is meant by "can be identified with" Background I was reading Anthony Henderson’s paper “Bases For Certain Cohomology Representations Of The Symmetric Group “ (Ref.: arxiv.org/pdf/math/0508162) and came across the following statement in Proposition 2.6 on Page 9: “V(1, n) can be...
  11. J

    Prove dual space has the direct sum decomposition

    What is the " o " in Voj? Definition. If V is a vector space over the field F and S is a subset of V, the annihilator of S is the set So of linear functionals f on V such that f(α) = 0 for every α in S. . . .
  12. J

    Prove dual space has the direct sum decomposition

    I apologize for not having any attempted work, but I have no idea how to even begin tackling this proof. Any direction would be greatly appreciated! Mike Homework Statement Let V be a vector space, Let W1, ..., Wk be subspaces of V, and, Let Vj = W1 + ... + Wj-1 + Wj+1 + ...
  13. J

    Solving PDE: Help with Advection-Diffusion Equation

    Homework Statement The Cauchy problem for the advection-diffusion equation is given by: u.sub.t + c u.sub.x = K u.sub.xx (−∞< x < ∞) u(x, 0) = Phi(x) where c and K are positive constants. The advection-diffusion equation essentially combines the effects of the transport...
  14. J

    Let v(x,t) = u(x+ct) and show that

    To your first point... I am sure it is: Let v(x,t) = u(x+ct,t) to your second point... That would mean the following is incorrect, right? v.sub.x(x,t) = c u.sub.x(x+ct,t) and should have been... v.sub.x(x,t) = u.sub.x(x+ct,t)
  15. J

    Let v(x,t) = u(x+ct) and show that

    Any help on any part will be GREATLY appreciated!
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