A dual purpose principal and minor component flow

Principal component flows are flows converging to the eigenvectors associated with the largest eigenvalues of a given symmetric matrix. Similarly, minor component flows converge to the eigenvectors associated with the smallest eigenvalues. Traditional flows required the matrix to be positive definite, and moreover, finding well-behaved minor component flows appeared to be harder and unrelated to the principal component case. This paper derives a flow which can be used to extract either the principal or the minor components and which does not require the matrix to be positive definite. The flow is shown to be a generalisation of the Oja-Brockett flow.