Question: what is the relationship between eigenvalues and singular values?
Answer: A nonnegative eigenvalue, λ ≥ 0, is also a singular value, σ = λ. The corresponding vectors are equal to each other, u = v = x. A negative eigenvalue, λ < 0, must reverse its sign to become a singular value, σ = |λ|. One of the corresponding singular vectors is the negative of the other, u = −v = x.