Let (mathcal {B}) denote the set of real symmetric matrices with spectrum σ, mathcal{B} = left{Q in mathbb{R}^{Ntimes N} | Q = P Sigma P^{-1}right}, (9).
The spatial semi-discretization of this kind of fractional derivatives often results in a coefficient matrix A with spectrum σ(A) satisfyingσ(A)⊆S:="{λ∈C:ℜ∈R}, where η>0 is a measure of dissipativity of the differential equations.
Our error bounds are much tighter than existing ones for matrices with rapid spectrum decay, and they justify the use of a constant amount of over-sampling relative to the rank parameter k, i.e, when the number of columns/rows is l = k + O(1).
In order to circumvent this problem, we enriched kinases using a sepharose matrix with immobilized broad spectrum kinase inhibitors (kinobeads) prior to quantitative MS analysis [ 16, 18].
According to results from frame and graph theory, the existence of an ETF depends on the existence of its signature matrix, that is, a symmetric matrix with certain structure and spectrum consisting of two distinct eigenvalues.
Therefore, the problem of designing an ETF can be reduced to an inverse eigenvalue problem, that is, the construction of a matrix with specific structure and spectrum consisting of two distinct eigenvalues.
The hoped-for comparison of the gas-phase IR spectra with the liquid-crystal matrix IR spectrum was frustrated, because the literature matrix spectrum seems most likely to be that of a protonated homodimer of the dipeptide rather than the protonated monomer.
The technique combining excitation emission matrix (EEM) spectra with parallel factor analysis (PARAFAC) was used to reveal the components of WEOM.
Soto and Rojo [6] investigated the existence of certain entrywise nonnegative matrices with a prescribed spectrum under certain conditions.
Since stochastic matrices are important nonnegative matrices, it is surely important to investigate the existence of stochastic matrices with a prescribed spectrum under certain conditions.
