I am using maple 13 to found Eingenvalues of an hermitian matrix :

M1:=Matrix([

> [lambda3+lambda4,0,0,0,0,0,lambda4/sqrt(2),0,0,I*lambda4/sqrt(2)],

> [0,lambda3/4,0,0,0,0,0,0,0,0],

> [0,0,lambda3/4,0,0,0,0,0,0,0],

> [0,0,0,lambda3/4,0,0,0,0,0,0],

> [0,0,0,0,lambda3/4,0,0,0,0,0],

> [0,0,0,0,0,lambda3,0,0,0,0],

> [lambda4/sqrt(2),0,0,0,0,0,lambda3/2,0,0,0],

> [0,0,0,0,0,0,0,lambda2,0,0],

> [0,0,0,0,0,0,0,0,lambda2,0],

> [-I*lambda4/sqrt(2),0,0,0,0,0,0,0,0,lambda4/2]

> ]);

>Eigenvalues(M1);

my surprise is that maple gives me 8 correct solutions an 2 complex eigenvalues which are not acceptable (we now that the eigenvalues for an hermitian matrix are all real) .

To understand the output of maple, first, I suspect that the complex part of the roots was null but without success I haven't found how to do it zero...

is it a bug? Thanks a lot to cooperation