- #1

- 102

- 14

I am currently trying to find the Eigensystem of the following 5x5 matrix in Mathematica. Unfortunately, doing so takes an insanely long time (I cannot even call Eigensystem[p][[1,1]] in a reasonable amount of time). Does anyone have any advice? Also I cannot simply redefine new variables for each of the differences x_{i}-x_{j} because I will need to solve for each x_{i} individually in an upcoming calculation so I do not think we can use some clever algebraic combination of the x_{i}-x_{j} to recover the x_{i} individually.

p = ({

{0, 1/(x1 - x2)^3, 1/(x1 - x3)^3, 1/(x1 - x4)^3, 1/(x1 - x5)^3},

{1/(x1 - x2)^3, 0, 1/(x2 - x3)^3, 1/(x2 - x4)^3, 1/(x2 - x5)^3},

{1/(x1 - x3)^3, 1/(x2 - x3)^3, 0, 1/(x3 - x4)^3, 1/(x3 - x5)^3},

{1/(x1 - x4)^3, 1/(x2 - x4)^3, 1/(x3 - x4)^3, 0, 1/(x4 - x5)^3},

{1/(x1 - x5)^3, 1/(x2 - x5)^3, 1/(x3 - x5)^3, 1/(x4 - x5)^3, 0}

});

Thanks!