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H is (P+M ×(P+M) channel matrix and V is (P+M ×1 noise vector.
where V X can be any L × L unitary matrix, and V Y can be any N × L orthonormal matrices.
Here the term triu denotes the upper triangular part of the concerned matrix and V is the intermediary variable.
where Σ is a 3 × 3 covariance matrix and v ¯ is the mean color in the RGB color space, obtained for the skin pixels within the expanded seeds.
We refer to (mathbf{G}= [ G_{alphabeta} ] inmathfrak {B} ( mathfrak{h} oplusmathfrak{h} ) ), as the coefficient matrix, and V as the left process generated by G.
where Z is the scaled data matrix, PCS is the principal component scores matrix, and V T is the transposed rotated loading (Eigenvectors) matrix.
Similar(33)
An offset address represented by 1r, vis located at the r th (0 ≤ r ≤ jp-1) row of the parity check H-matrix and v th (0 ≤ v ≤ k-1) column in which k circulant permutation sub-matrices are placed.
We then compute a new M matrix using the modified S matrix and the same matrices U and V as obtained from the original M matrix.
Let w ∈ R 3 be the eigenvector of H with respect to eigenvalue −1, that is, H w = − w ; v ∈ R 3 be the adjoint eigenvector of H T that is, H T v = − v where H T is the transposed matrix, and 〈 v, w 〉 = 1, where 〈 ⋅, ⋅ 〉 is the standard scalar product in R 3.
It is the work of the production designer Owen Paterson, who also worked on the "Matrix" films and "V for Vendetta".
where (boldsymbol {bar {v}}_{i}in mathbb {C}^{1times M}) is the ith row vector of matrix V and v i,m is the m-th element in the row vector (boldsymbol {bar {v}}_{i}).
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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