complex – Simplifying away imaginary part


B = {{17/3, 1/3, 1/3, 1/3}, {1/3, 1/3, 1/3, 1/3}, {1/3, 1/3, 1/3, 1/3}, {1/3, 
    1/3, 1/3, 82/3}};
A = {{5/3, 0, 1/3, 0}, {0, 5/3, 0, 1/3}, {1/3, 0, 10/3, 0}, {0, 1/3, 0, 
    10/3}};

val = First /@ Eigensystem({B, A}, 1);

All of the values are real

valR = val // RootReduce

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Element(valR, Reals)

(* True *)

valR // N

(* {8.33542, {0.0311157, -0.179391, 0.00719285, 1.}} *)

However, if represented using radicals, they must use complex numbers (see Casus irreducibilis)

valR // ToRadicals

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