# Strange answer for Eigenvalues of a 4x4 matrix [duplicate]

This question already has an answer here:

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

 mymatrix = {{1 - a, -((I Conjugate[b])/Sqrt), b/Sqrt[
2], -((I a)/2)}, {(I b)/Sqrt, 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?

## marked as duplicate by Szabolcs, b.gates.you.know.what, J. M. is away♦Mar 1 at 9:10

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• Did you look up Root in the documentation? – Szabolcs Mar 1 at 8:55

## 1 Answer

The following works.

mymatrix = {{1 - a, -((I Conjugate[b])/Sqrt), b/Sqrt[
2], -((I a)/2)}, {(I b)/Sqrt, 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.

• ToRadicals[] is mentioned in this answer. – J. M. is away Mar 1 at 9:43
• @J. M. is computer-less: Thank you. – user64494 Mar 1 at 10:08