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where z ̄ ′′ is of dimension n×1.
The final descriptor vector is of dimension 64: 4×4 regions with four parts per region.
It is easy to see that any almost quaternionic manifold is of dimension 4m, m ≥ 1.
It is easy to see that such a manifold is of dimension 4m, (mgeq1).
From the definition above, matrix Λ h is of dimension K×K.
Note, however, that the system of equations is of dimension | S |.
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According to the government statistics office, unlawful construction in Italy is of "dimensions unparalleled in other advanced economies".
Q is of dimensions (|I| times f) and (P^T) is of dimensions (f times |U|), where f is the number of latent factors.
COW works by filling a zero-indexed matrix Γ, which is of dimensions m+1 by | d|+1.
Matrices and are of dimension and they are given by (11).
To this end, let C π ′ ∩ B s be of dimension s.
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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