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The φ matrix has full column rank, i.e., rank=N r N t KL=8.
If a matrix has full rank, there is no vector z ≠ 0 such that S z = 0.
From (1), it can be easily shown that the controllability matrix has full rank and the system is controllable.
The matrix H 2p has the same form as (10) in order that the parity part of the matrix has full rank, but with distinct random cyclic shifts [8].
The latter is hard to enforce on non-conforming meshes (cf. Section 6) and it is simpler to gauge the formulation (1 - 2) or to add a regularization term to (1) so that the system matrix has full rank.
Although in theory, under the above stated conditions, the matrix has full rank for any number of users,, the matrix condition number may become too high when CFOs or delay differences between users become small.
Similar(45)
This leads to a sufficient and necessary condition of a certain estimability Gramian matrix having full rank.
However, we have to note that this condition is only true for the case where the correlation matrices have full rank.
We can see that being trained to generalize like the teacher network using soft targets produces hidden layer weight matrices having fuller rank than training with hard targets.
An investigation into the hidden layer weight matrices finds that soft target-trained networks tend to produce weight matrices having fuller rank and slower decay in singular values than their hard target-trained counterparts, suggesting that more of the network's capacity is utilized for learning additional information giving better accuracy.
Hence, from (44) matrix φ has full column rank matrix with rank=N r N t KL.
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