If a square matrix A is real and symmetric, then the eigenvalues

1. are always real
2. are always real and positive
3. are always real and non-negative
4. occur in complex conjugate pairs

(A – λI) = 0

A =		a			b
		b			a

Now		a-λ			b		= 0
		b			a-λ

which gives (a – λ)² – b² = 0
⇒ a – λ = ± b
⇒ λ = a ± b
Hence eigen values of the matrix are real.