The method is described in relation to writing differential vectorized equations of the electromechanical process behavior; choice of physical variables to be controlled; writing state-space linear equations in continuous-time, state space equation discretization, and projecting discretized state-space equations into the eigenvector basis of the evolution matrix; discretized state-space equation inversion and calculation of the input equation; and control development, real-time implementation, initial state-space prediction, control under constraints, and examples.

After each match simulation, a rating for each player in the network was calculated using eigenvector centrality, a measure of the importance of a particular node (player) in a network (team)--that is, by determining the extent to which player i interacted with other central players.

There were also less-popular outliers who had fewer social interactions and a lower eigenvector.

For this analysis, data were first standardized and a correlation matrix, eigenvalues, and eigenvectors were calculated using NTSYS-pc verson 2.

1]) is complete and orthogonal in the n-dimensional vector space, but only the first eigenvalue and the first eigenvector have physical meaning.

The theorem states that if we have a "suspected eigenpair" ([mu],x) with small residual, then x is indeed close to an eigenvector (or to the invariant subspace associated with the cluster) provided that [mu] is sufficiently far away from the remaining eigenvalues.

Then the first eigenvector contains weights, or factor loadings, that yield the linear combination of the prices in P with the largest variance, restricting the sum of the squared weights to equal one.

includes chapters on Gaussian elimination and its variants, sensitivity of linear systems, the least squares problem, the singular value decomposition, eigenvalues and eigenvectors, and iterative methods for linear systems.