Strange answer for Eigenvalues of a 4x4 matrix

Question

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?

Did you look up Root in the documentation? – Szabolcs Mar 01 '19 at 08:55 — Szabolcs, Mar 01 '19 at 08:55

user64494 · Answer 1 · 2019-03-01T09:17:32.840

0

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.

edited Mar 01 '19 at 09:17

answered Mar 01 '19 at 08:57

user64494

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ToRadicals[] is mentioned in this answer. – J. M.'s missing motivation Mar 01 '19 at 09:43
@J. M. is computer-less: Thank you. – user64494 Mar 01 '19 at 10:08

Strange answer for Eigenvalues of a 4x4 matrix

1 Answers1