# what do those signs #1, #1^2, #1^3, & mean here? [duplicate]

I have read common pitfalls page and the documentation page but I still don't understand what do those signs mean here?

A = {{0.472, 0.008 + 0.01 I, 0.056 - 0.029 I}, {0.008 - 0.01 I, 0.235,
0.003 - 0.002 I}, {0.056 + 0.029 I, 0.003 + 0.002 I, 0.293}};
Cvol = {{1, 0, 1/3}, {0, 2/3, 0}, {1/3, 0, 1}};
Eigenvalues[A - a*Cvol]
(*{1. Root[(-0.0531814 -
2.9302*10^-20 I) + (0.439425 -
6.61797*10^-19 I) a - (1.17112 + 0. I) a^2 +
1. a^3 + ((0.529735 - 3.65918*10^-19 I) - (2.88169 + 0. I) a +
3.75 a^2) #1 + (-1.6875 + 4.5 a) #1^2 + 1.6875 #1^3 &, 1],
1. Root[(-0.0531814 -
2.9302*10^-20 I) + (0.439425 -
6.61797*10^-19 I) a - (1.17112 + 0. I) a^2 +
1. a^3 + ((0.529735 - 3.65918*10^-19 I) - (2.88169 + 0. I) a +
3.75 a^2) #1 + (-1.6875 + 4.5 a) #1^2 + 1.6875 #1^3 &, 2],
1. Root[(-0.0531814 -
2.9302*10^-20 I) + (0.439425 -
6.61797*10^-19 I) a - (1.17112 + 0. I) a^2 +
1. a^3 + ((0.529735 - 3.65918*10^-19 I) - (2.88169 + 0. I) a +
3.75 a^2) #1 + (-1.6875 + 4.5 a) #1^2 + 1.6875 #1^3 &, 3]}*)

• Likely duplicates: (13767), (19035) Feb 6 '16 at 13:52

The solution to your Eigenvalues function are Root objects, see the documentation.
Root[f,k] represents the exact k^(th) root of the polynomial equation f[x]==0.
Inside Root is the pure function in the argument #1. If we named this pure function f with argument x, this would correspond to the situation in the above quote with f[x].
Your Matrix $A$ is from $\mathbb{C}^{3\times 3}$, so the eigenvalues are solutions of the characteristic polynomial of order $3$. The #1, according to the documentation
Because of the parameter a mathematica returns an abstract Root object instead of a closed solution.