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Verify eigenvalues of a TST matrix

  1. May 13, 2015 #1
    1. The problem statement, all variables and given/known data

    I have ##A=TST(-1,2-1),## and I need to show that an eigenvector of A is,##Y_{j}=sin(kj \pi / J).##
    and then find the full set of eigenvalues of A.

    The matrix A comes from writing ##-U_{j-1}+2U-U_{j+1}=h^{2}f(x_{j}), 1\le j \le J-1##, in the form ##AU=b##

    2. Relevant equations

    The above.


    3. The attempt at a solution

    Since the TST is a j-1 x j-1 dimensional, I'm unsure how to approach the algebra.

    I'm unsure how to get started, and the notation is confusing me too- I know that the eigenvalues of a ##TST(\alpha, \beta)## are ##\alpha+2\beta cos(k\pi/m+1)## where ##k=1....m##,

    so here do I need to take ##k=j## and ##m+1=J##, but this doesn't really make sense to be as in the above, ##k## and ##m## are anything just with the contrainst ##k=1....m##, aren't they?

    i'm unsure how to construct the eigenvector ##Y##, should it be ##AY_{j}= A (Y_{0},....,Y_{J})^{T}##,
    so ##j## runs from ##1## to ##J-1##?

    Any help really appreciated ! Thanks alot !
     
  2. jcsd
  3. May 13, 2015 #2

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    What does TST mean?
     
  4. May 13, 2015 #3

    Mark44

    Staff: Mentor

    I don't know what TST means either. Don't assume that an acronym you use is understood by all.
     
  5. May 13, 2015 #4
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