Suppose I have the following symbolic 7 * 7 matrix

```
mat= {{(a^2 b^2)/c^2, 0, 0, 0, 0, 0, (a^2 b^2 e11)/c^2}, {0, (a^2 b^2)/c^2,
0, 0, 0, 0, (a^2 b^2 e22)/c^2}, {0, 0, (a^2 b^2)/c^2, 0, 0, 0, (
a^2 b^2 e33)/c^2}, {0, 0, 0, (2 a^2 b^2)/c^2, 0, 0, (2 a^2 b^2 e12)/
c^2}, {0, 0, 0, 0, (2 a^2 b^2)/c^2, 0, (2 a^2 b^2 e13)/c^2}, {0, 0,
0, 0, 0, (2 a^2 b^2)/c^2, (2 a^2 b^2 e23)/c^2}, {(a^2 b^2 e11)/
c^2, (a^2 b^2 e22)/c^2, (a^2 b^2 e33)/c^2, (2 a^2 b^2 e12)/c^2, (
2 a^2 b^2 e13)/c^2, (2 a^2 b^2 e23)/c^2,
b^2 (1 + (
a^2 (e11^2 + 2 e12^2 + 2 e13^2 + e22^2 + 2 e23^2 + e33^2))/c^2)}}
```

for which I have the following information

a> 0, b> 0, c> 0, {e11, e22, e33, e12, e13, e23} are real.

How is it possible to symbolically get the square root of this matrix?

What I've tried so far has been to compose the matrix myself, but it doesn't give me a closed solution, although I declare the assumptions above, i.e. H.

```
eigen= Assuming({e11,e22,e33,e12,e13,e23}(Element)Reals&&a>0&&b>0&&c>0,Eigenvalues(mat));
```

Are there other ways I can find the square root of this symbolic matrix?