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Williamson matrices have some unbalanced rows and are avoided.
Compared with the conventional random matrices, sparse binary matrices have some attractive properties, such as lower storage/encoding cost and easy hardware implementation.
It is shown that both of procedures and results for the partition tree derived from interval-valued and crisp-valued similarity relation matrices have some corresponding relationships and different merits.
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The determination of tetracycline by fluorescence spectrophotometry in complex matrices has some difficulties, because the presence of other compounds in the matrix affects the analytical signal.
A modified Gaussian elimination was developed to solve a band matrix having some off-band submatrices.
It is obvious that, because of its additive nature, the iWSD method does not work rather good if the initial matrix has some very small entries together with some very large ones (a practically important case!).
Thus, one can assert that improved WSRD method has some advantage among the other methods of matrix updating in practically important situations when the initial matrix has some very small entries and some very large ones simultaneously (because of multiplicative nature of iWSRD objective function).
In the case that such a matrix has some pair of complex conjugate eigenvalues then the solution is bounded and the solution trajectory may oscillate, and if there is some eigenvalue with positive real part (i.e., within the instability region), then the state trajectory solution is unbounded.
The presence of reinforcement in the polymeric matrix has some influence on the crystalline regions, since slightly more perfect crystals seem to be obtained in the composites with not very high glass fibre content, judging from the better resolution of the (110) diffraction and from the slightly higher melting temperatures.
This suggested that the shape of this matrix had some particularities, and in fact Table 1 shows that the first and second eigenvalues for this sample were unusually small and large, respectively.
Therefore, some matrices have been proved to be incoherent enough with any fixed sparsifying basis Ψ with overwhelming probability, such as Gaussians or ±1 random matrices [16].
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com