Eigen values of a real symmetric matrix are always A. positive B. negative C. real D. complex

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.