Eigenvalues of a matrix whose elements are given as the sum of the product of another matrix's eigenvalues times some real coefficients

Question

The title is quite long but I wouldn't know how to explain this otherwise.

I have been working on this paper for quite some time, https://www.sciencedirect.com/.../pii/0393044088900319, and I can't understand how equation (26) implies equation (27) (reference 9 is to a book called "The Theory of Matrices" by Gantmakher).

The equations in question

It seems to me that this comes from some Linear Algebra concept that I must have obviously forgotten and that I can't quite find without proper reference. I would really appreciate any help!