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Thus, it is difficult to find the globally optimum transmit covariance matrices that achieve the capacity.
In numerical analysis it is often necessary to estimate the condition number CN(T)="‖T‖⋅‖T−1‖ and the norm of the resolvent ∥∥(ζ−T −1∥∥ of a given n×n matrix T. We derive new spectral estimates for these quantities and compute explicit matrices that achieve our bounds.
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(i)We derive the optimal joint design of the BS and RS filter matrices that achieves the minimum mean squared error (MMSE) for both downlink and uplink of the multiuser MIMO relay systems at the absence of direct path.
The low-density burst-oriented generator matrix (LDBOGM) is the H matrix that achieves the best GRM(H) value that our algorithm is able to reach.
Thus, the MMSE algorithm is equivalent to the choice of the K × K matrix M that achieves M = arg min M ∈ R K × K E | | b − M y | | 2. (11).
Let be the positive-definite error covariance matrix for an estimator that achieves the CRLB.
We then parametrize the class of pure Gaussian state covariance matrices that can be achieved by this particular type of linear quantum system.
Strategies to provide smart capabilities to the composite biomaterials primarily seek to achieve matrices that are instructive/inductive to cells, or that stimulate/trigger target cell responses that are crucial in the tissue regeneration processes.
The second root of all square matrices that have different eigenvalues are achieved.
In this context, the number of different scores that the matrix can achieve is significantly larger.
Terbium ions were incorporated into new organic-inorganic matrices to achieve intense green emissions.
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Justyna Jupowicz-Kozak
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