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The above results can easily be extended to the finite number of matrices as in the following corollary.
Proposition 3 Each characteristic polynomial obtained from 2 × 2 matrices, as in system (5), appears to be a congruence class.
The SVM method was surprisingly efficient even for a small learning set and series generated directly from matrices as in (11).
Hydrogels can present many different physical forms including solid molded forms, such as soft contact lenses, pressed powder matrices, as in pills or capsules, or different types of microparticles and coatings, or liquids, that form gels upon cooling or heating.
For case (b), Double Cantilever Beam (DCB) experiments were used to obtain the fracture toughness of the unidirectional laminates with the HP-NGP reinforced matrices as in (a), in accordance with ASTM D5528.
Wood (2009) additively decomposed the Leontief inverse itself into three determinants: backward and forward linkage vectors and an industrial structure matrix, which was obtained by dividing the Leontief inverse into two matrices, as in the RAS method.
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Combining calcium chloride with an alginate to make a water-insoluble matrix (as in "squid caviar") is a standard procedure in many industries.
Calculate the covariance matrix as in (6).
The matrix R t is a symmetric Toeplitz matrix as in Equation (9).
The sensing matrix is a square full-rank matrix as in [17].
LPCA can be summarized as follows: 1. Calculate the covariance matrix as in (6). 2.
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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