Complex representation of eigenvalues of a symbolic 2x2 matrix

Creating following matrix

syms a
A = [0, 1;
    -1, 2*cos(a)];

and taking out its eigenvalues

lambda = eig(A)

the result I get is

lambda =
cos(a) + ((cos(a) - 1)*(cos(a) + 1))^(1/2)
cos(a) - ((cos(a) - 1)*(cos(a) + 1))^(1/2)

but I expect to see

lambda =
cos(a) + sin(a)*1i
cos(a) - sin(a)*1i

What should I do?

Answer 1

[Star Strider]

This is likely as close as it is possible to get —

syms a
A = [0, 1;
    -1, 2*cos(a)];

lambda = eig(A)

lambda = 

lambda = simplify(rewrite(lambda, 'sin'), 500)

lambda = 

Otherwise use the subs function to change to .

.

Answer 2

[Paul]

Is the expected result obtained only when a is real?

syms a
A = [0, 1;
    -1, 2*cos(a)];
lambda = rewrite(simplify(eig(A),100),'sin')

lambda = 

simplify(lambda)

ans = 

Now add the additional assumption on a:

assume(a,'real')
simplify(lambda)

ans =