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Table 1 presents the correlation matrices, means, and standard deviations for the models forecasting externalizing and internalizing symptoms.
The latter affords ample motivation for studying weak equivalence for arbitrary primitive matrices and not just those that match unimodal kneading sequences.
The amplitudes of incoming and outgoing modes for both fields are related by scattering matrices.
Connected simple systems, transition matrices and heteroclinic bifurcations.
In the case of the orthogonal group the generators must be skew symmetric matrices.
The present paper offers a better solution to this problem, using density matrices and superoperators instead of probability distributions.
To relate the sign of diagonal elements to the sign of the real parts of eigenvalues, we introduce the following dominant diagonal properties of matrices.
All operations are organised in relation to this base: in particular, they can be represented by linear functions whose matrices are diagonal in this base.
In that case, the simplest option is to take the canonical viewpoint, that is, the one consisting of diagonal matrices.
Fully off-diagonal submatrices of diagonally dominant matrices are completely unstructured matrices, and so with irreducible determinants of unbounded degree.
In the present work we give another construction for low-rank co-diagonal matrices, based on a modular sieve formula.
In this method it is not necessary to consider polarization vectors and eigenvalues of dispersion matrices around coupling points.
Distance matrices were calculated with a 50% conservation filter for each phylogenetic group.
Distance matrices between isolates were created for each type of data as follows.
Blocked matrices can never lead to a solution.