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Exact(3)
From here onwards, we assume that the numbers in the matrix are such cardinal utilities).
where (norm-dependent) and (provided that is a stability matrix) are such that, for instance, for the supremum on of the vector (and induced matrix) norm, so that (2.15) becomes (2.16).
And the zeroth terms of the coefficient matrix are such that a(0) = 1, b(0) = 0, c(0) = 0 and d(0) = 1.
Similar(57)
In developed countries, the population matrix is such that about 45% of the women population is above 50.
The new parity matrix is such that all its submatrices are invertible.
where, and the matrix is such that its th row has a at the th column and zeroes elsewhere.
Thus, the cost matrix is such that its diagonal elements are all zeros and the off-diagonal elements are all ones.
\end{align} Matrix multiplication satisfies the rules (AB C = A BC) (associativity), and (A+B C = AC+BC as well as C(A+B) = CA+CB (left and right distributivity), whenever the size of the matrices is such that the various products are defined.
By introducing extra slack variables, the Lyapunov matrix and the system matrix are decoupled such that the controller parametrization is independent of the Lyapunov matrix.
The rows/columns of the matrix are ordered such that similar rows/columns are near each other.
This matrix is used as a similarity measure for a subsequent hierarchical clustering procedure where the rows and columns of the matrix are reordered such that patients with similar co-clustering patterns become neighbors.
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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