The real() command outputs a complex number (doesn't appear to change it).

I want to evaluate the real part of some eigenvalues, but real(eigen) just returns eigen (isreal(real(eigen) returns 0).

[Stephen23]

Why do you imagine that ISREAL() can be applied to symbolic variables? It is not listed as a function of the symbolic toolbox:

https://www.mathworks.com/help/symbolic/referencelist.html

and the ISREAL() documentation clearly states that it checks "whether array uses complex storage", i.e. it checks for something that is purely a characteristic of numeric arrays and has nothing to do with symbolic mathematics. See:

https://www.mathworks.com/help/matlab/ref/isreal.html

In contrast, REAL() is a function of the symbolic toolbox, and works exactly as described:

https://www.mathworks.com/help/symbolic/real.html

[Paul]

Just because a function is not listed as a function of the symbolic toolbox in its documentation does not mean that function can't be applied to a sym variable. We can further break this situation down into two cases.

First, functions that are not methods of the syms class, but work fine on sym objects because the underlying code in the function all works on sym. The function dot is a good example

x = sym('x',[1 3])

x = 

dot(x,x)

ans = 

Second, some methods of the sym class (at least one, I can't say for sure more than one) are just not documented. For example, exp is a sym method, but is (shockingly, IMO) not listed as a function of the symbolic toolbox on that linked page.

exp(x)

ans = 

More discussion here

Answer 1

[Torsten]

isreal(real(double(eigen(t))))

instead of

isreal(real(eigen(t)))

Answer 2

[Paul]

In syms world, use isAlways to determine if an expression or variable is real, etc.

syms x
isAlways(in(x,'real'))

Warning: Unable to prove 'in(x, 'real')'.

ans = logical
   0

assume(x,'real')
isAlways(in(x,'real'))

ans = logical
   1

[Stephen23]

+1 for giving the correct symbolic solution.