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So the gain matrices are all real matrices.
Obviously, the diagonal elements in the payoff matrices are all zero since collision yields zero reward.
In addition, to keep the illustration simple and focused, we assume the channel coefficient matrices are all full rank.
Regarding the interconnection weights, they do not require any network training, so the weigh matrices are all initialized to zero.
X ˜ Open image in new window can be defined by nine matrices, and the elements of these matrices are all crisp numbers.
In the remaining of this paper, the symbol tilde is omitted, whereas the SV coefficient vectors and matrices are all based on the modified basis, unless otherwise noted.
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Note that the optimal covariance matrices were all proportional to the identity matrix Σ ^ ∝ I and are thus summarised by a single value, the variance of expression of the corresponding cluster.
Unlike the matrix for 'I', the horizontal rows of this 2D matrix are all exactly the same.
For these networks, the eigenvalues of the outer coupling matrix are all non-positive.
Every M-matrix is invertible, and the entries of its inverse matrix are all positive numbers.
It is assumed that the particle, interphase and matrix are all inclusions of composites.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com