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In general, every generalized matrix < A, B > can be turned into a closed-set system by adding to B ∪ {A} the intersections of arbitrary nonempty families, and therefore into an abstract logic, which we denote by < A, C(B)>.
This paper investigates the generalized matrix projective synchronization problem of general colored networks with different-dimensional node dynamics.
Detailed derivation of a generalized matrix equation is given.
A generalized matrix is reduced if its Tarski congruence is the identity.
In a similar way the systematic study of bases for generalized matrix models of a logic becomes important.
The resulting generalized matrix eigenvalue problem is large, sparse and non-Hermitian.
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In the next section we will expound the semantics of abstract logics and generalized matrices that serves to develop a really general theory of the algebraization of logic systems.
The model formulation is concise and consistent with the generalized matrix-based LCA model; its linearity also makes identification of the optimal solution straightforward.
These generalized matrices (and their corresponding abstract logics) are called full models.
The generalized matrices < A, B > that correspond to abstract logics have the properties that A ∈ B and that B is closed under intersections of arbitrary nonempty families.
(Sigma^) represent the generalized inverse matrix of the matrix Σ.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com