I have read in my lecture notes on *Mathematica* that functions (in the general sense) can be applied to lists of data and that they can return new lists with data. I have tried this and I have got these results, see following picture:

[![enter image description here](https://i.stack.imgur.com/2I5cB.gif)](https://i.stack.imgur.com/2I5cB.gif)

As you can see, in this picture the function `Sin[x]` works fine on the lists but the functions `Eigenvalues` and `Characteristic` polynomials they do not...

Do I miss something here or am I wrong at all?

Thanks.