Problem in Eigensystem in Mathematica

• Mathematica

Main Question or Discussion Point

Hello.
In Mathematica, I'm trying to find the eigenvalues and eigenvectors of a 10x10 matrices that is diagonalizable for sure.
The matrix ix:
{{0, 0, 0, 0, -2 t, -2 t, -2 t, -2 t, 0, 0}, {0, 0, 0, 0, -t, t, -t,
t, 0, 0}, {0, 0, 2 U, 0, -t, t, -t, t, 0, 0}, {0, 0, 0, 2 U, -2 t,
2 t, -2 t, 2 t, 0, 0}, {-Sqrt[2] t, -t, -t, -Sqrt[2] t, U, 0, 0,
0, -t, -t}, {-Sqrt[2] t, t, t, Sqrt[2] t, 0, U, 0,
0, -t, -t}, {-Sqrt[2] t, -t, -t, -Sqrt[2] t, 0, 0, U,
0, -t, -t}, {-Sqrt[2] t, t, t, Sqrt[2] t, 0, 0, 0, U, -t, -t}, {0,
0, 0, 0, -t, -t, -t, -t, U, 0}, {0, 0, 0, 0, -t, -t, -t, -t, 0, U}}
where t and U are both Reals.

The command I use is: Assuming[t \[Element] Reals,
Assuming[U \[Element] Reals, Eigensystem[MATRIXNAME]]]

I'm getting some symbols that I don't know. For example, one of the eigenvalues is:
Root[8 t^2 U - 8 t^2 #1 - 8 Sqrt[2] t^2 #1 + 2 U^2 #1 -
3 U #1^2 + #1^3 &, 1]
What are these # and &? What does mean "Root[expression, 1]" ?

Regards,
Marcus.