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I am getting these strange eigenvalues of this simple looking 4-dimensional matrix:

 mymatrix = {{1 - a, -((I Conjugate[b])/Sqrt[2]), b/Sqrt[
    2], -((I a)/2)}, {(I b)/Sqrt[2], a/2, 0, 0}, {Conjugate[b]/Sqrt[
    2], 0, a/2, 0}, {(I a)/2, 0, 0, 0}};
Eigenvalues[mymatrix]
    (**{a/2, Root[
  a^3 + (4 a - 6 a^2 - 8 b Conjugate[b]) #1 + (-8 + 4 a) #1^2 + 
    8 #1^3 &, 1], 
 Root[a^3 + (4 a - 6 a^2 - 8 b Conjugate[b]) #1 + (-8 + 4 a) #1^2 + 
    8 #1^3 &, 2], 
 Root[a^3 + (4 a - 6 a^2 - 8 b Conjugate[b]) #1 + (-8 + 4 a) #1^2 + 
    8 #1^3 &, 3]})

What to do with this Root[] stuff?

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  • $\begingroup$ Did you look up Root in the documentation? $\endgroup$
    – Szabolcs
    Mar 1, 2019 at 8:55

1 Answer 1

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The following works.

mymatrix = {{1 - a, -((I Conjugate[b])/Sqrt[2]), b/Sqrt[
2], -((I a)/2)}, {(I b)/Sqrt[2], a/2, 0, 0}, {Conjugate[b]/Sqrt[
2], 0, a/2, 0}, {(I a)/2, 0, 0, 0}};Eigenvalues[mymatrix]//ToRadicals

Addition. I don't see that way in How to work with Root objects as well as in the help to Root.

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