positive
negative
real
complex
Answer is Right!
Answer is Wrong!
The correct answer is C. real.
A real symmetric matrix is a square matrix that is equal to its transpose. The eigenvalues of a real symmetric matrix are always real numbers. This is because the eigenvalues of a matrix are the roots of its characteristic polynomial, and the characteristic polynomial of a real symmetric matrix is always a real polynomial.
Option A is incorrect because the eigenvalues of a real symmetric matrix can be positive, negative, or zero.
Option B is incorrect because the eigenvalues of a real symmetric matrix can be negative.
Option D is incorrect because the eigenvalues of a real symmetric matrix are always real numbers.