how can we find eigen values and eigen vector of a matrix having variable like x or y ?

how can we find eigen values and eigen vector of a matrix having variable like x or y ?

we have matix

a = [ 2, 1+z^-1 ; z+1 2];

i want to find eigen values of a.

Answer 1

[Raj]

You need to have 'Symbolic Math toolbox' to do this. Then you can calculate the Eigen values & Eigen vectors in terms of the variables something like this:

syms z; 
a = [ 2, 1+z^-1 ;  z+1 2];
[V,D]=eig(A);

Answer 2

[Hiro Yoshino]

a is supposed to be in its size otherwise you can calculate neither eigen values nor eigen vectors to begin with.

[Raj]

Correct but the 'a' matrix given in question is a 2x2 matrix. So the matrix is square and I don't see any problem here.