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The eigenvalues λ1,..., λ M of a M × M covariance matrix are always indexed such that λ1≥ λ2... ≥ λ M, and the corresponding KLT matrix has the structure T = ( u 1 T, …, u M T ), where u m is the eigenvector associated λ m.
Therefore, if the squared norm of hierarchical signal differences with indices not being in the same row of XC matrix are always larger or equal than the bound, ∥ u c A c B - u c A ′ c B ′ ∥ 2 ≥ | α | 2 δ min 2, (21).
The diagonal elements of the similarity matrix are always 1, indicating that each centroid is most similar to itself.
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A Liberty spokesperson said: "The gangs matrix was always a poorly-designed and biased scheme carrying huge repercussions for those on it, 87% of whom are from black and ethnic minority communities.
The system matrix is always symmetric regardless of the boundary shape of the membrane, and the calculated eigenvalues rapidly converge to the exact values thanks to the special function employed in this study.
A blank matrix is always desired for all types of quantitative analyses.
Moreover, we assume that the input matrix is always nonsingular when the supporting foot makes flat contact with the ground and that the contact force is always feasible.
Because the total variability matrix is always a low-rank rectangular matrix, a dimension reduction process is also imposed by the i-vector extractor [12].
This network guarantees that, while rows are loaded in RB in different positions, the register matrix is always fed with an ordered column of pixels.
The output SNR with the maximum SNR filtering matrix is always greater than or equal to the input SNR, i.e., oSNR H max ′ ≥ iSNR.
The output SNR with the tradeoff filtering matrix is always greater than or equal to the input SNR, i.e., oSNR HT,μ ≥iSNR, ∀μ>0.
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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