[amp_mcq option1=”positive” option2=”negative” option3=”real” option4=”complex” correct=”option3″]
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.