It is a non-trivial problem to decompose the matrix S into matrices C and Δ; in the most general case such matrix decomposition does not have a unique solution.
One notable feature is that the combination takes the most general form with matrix weights.
As π is not necessarily multiplicative, then the TF form is the most general reversible rate matrix for dinucleotides in the class of models where each substitution event involves only one nucleotide.
For multi-stream transmission the combiner can be defined per transmission layer, or in the most general form, as a matrix of dimension r k ×r k, where the off diagonal elements characterize the inter-layer effects.
Possible extensions of M0, for example with an individual λ for group effects or – in the most general form – using an identity matrix instead of G A, e.g. [ 39], as well as an individual λ for group effects were beyond the scope of this paper.
The most general form for the genetic variance matrix from MET data is a fully unstructured matrix with p (p + 1)/2 parameters where p is the number of environments, and this matrix is, by definition, nonnegative definite.
Symplectic difference systems are discrete counterparts of linear Hamiltonian differential systems z ′ = J H ( t ) z. with the Hermitean matrix ℋ, i.e., H ∗ = H, in the sense that they are the most general first-order systems whose fundamental matrix is symplectic.
Finally, recall that this invertible matrix in the most general form is given by a combination of steady-state assumptions and the sum containing the conserved moiety.
For the Open system, the most general model we could use to generate the transition parameters for the matrix contained at most 145 parameters (12·12+1 parameter to account for probability of capture).
Moreover, by using the presently developed mixed formalism, the explicit expressions for the fundamental matrix and eigenvectors are obtained first time for the most general composite laminates.
