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Using a contrast matrix, paired comparisons of senescent vs. young HUVECs were calculated for each donor and tested for significance using moderated hypothesis tests (moderated t-statistic) as available in LIMMA.
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Thus, each segment is now represented by the matrix pair.
Our results demonstrate that the combination of the filler-polymeric matrix pair chosen is crucial.
This implies the spectrum of matrix pair ( E, A ) and ( E ˜, A ˜ ) must also coincide.
Let (A,Binmathbb{C}^{ntimes n}), (ngeq2) and ((A,B)) be a regular matrix pair.
In this paper, we focus on matrix Greub-Rheinboldt inequalities for commutative positive definite Hermitian matrix pairs.
In this paper, we introduce some new bounds for several Kantorovich-type inequalities for commutative positive definite Hermitian matrix pairs.
A matrix pair ((A, B)) is called regular if (operatorname{det} A-zB) neq0 ), and otherwise singular.
Hence, we cannot use the method in [2] to estimate the generalized eigenvalues of the matrix pair (A,B).
In this section, a set is provided to locate all the generalized eigenvalue of a matrix pair.
Many researchers are interested in the localization of all generalized eigenvalues of a matrix pair; see [1, 2, 6, 7].
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