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First, we deal with the more general matrix corona problem.
In this paper, we propose to use a more general matrix method to obtain necessary and sufficient conditions to sum the conjugate derived Fourier series.
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More general matrices can be considered if we assume cross-couplings between the transmit and/or receive antenna elements.
Furthermore, one can obtain more general conclusion corresponding to the results of this paper by taking more general matrices instead of the Fibonacci matrix.
The optimal design problem corresponds to a linear optimality criterion for a specific matrix L. In the present paper these results are extended to more general matrices L. By our results the optimal design problem for a Fourier regression of large degree can be reduced to a design problem in a model of lower degree, which allows the determination of L-optimal designs in many important cases.
However, to our knowledge, the generalized reflexive solution to the more general coupled matrix equation (1) and the optimal approximation reflexive solution have not been derived.
Concrete representations involving the Pauli matrices and more general gamma matrices are an integral part of the physical description of fermions, which behave as spinors.
The terms E2 and E3 would likely decrease though as the covariance matrix Σ relaxes the correlation terms that renders it too rigid a fit for the self class into a more general uncorrelated matrix.
Other intermediate models include Kimura's "Stepping Stones" model [ 12, 13] and the more general "Migration Matrix" which encapsulates geographic (or other) barriers to migration [ 14].
We have demonstrated the algebra for easily accommodating the absence of particular sectors in a region and the choice among alternative technologies through the replacement of the identity matrix I by the more general I ∗ matrix and the square A matrix by A ∗. To choose among alternative technologies is a task for the model, not the database.
Now, the second result in this section is an inequality for a more general tridiagonal operator matrix than the previous one.
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