S -Orthogonal Projection Operators as Asymptotic Solutions of a Class of Matrix Differential Equations
Erkki Oja · SIAM Journal on Mathematical Analysis · 1978
A class of nonlinear autonomous matrix differential equations is considered. Two special cases of this class yield the differential equations of adaptive network models which were initially introduced in connection with idealized neuron networks. It is shown that these equations exhibit an asymptotic behavior that is intimately related with the matrix form of the Gram–Schmidt orthogonalization algorithm in a real vector space, with respect to an inner product with an arbitrary positive definite symmetric weight matrix S.