Sentence examples for matrices we derive from inspiring English sources

In section "Design of MIMO processing matrices", we derive the MIMO processing matrices and in the section "Numerical results", we present the results of simulations.

Based on the Takagi factorization of complex symmetric matrices, we derive algorithm for computing the partial orthogonal rank-one decomposition of complex symmetric tensors with an order being a power of two, denoted by CSTPOROD.

In this paper, based on the property of the circular matrix we derive a framework of rate analysis for SC-FDMA and OFDMA, which is a generalization of the result in [3], and it allows for the calculation of the achievable rate using arbitrary sub-carrier assignment methods in both the single user system and the multi-user system subject to individual power constraints of the users.

From this matrix, we derive least-cost distances from the geographical origin of the crop and use these to predict the age of archaeological crop remains and the heterozygosity of crop populations.

Here, using LRA upon the obtained protein feature matrix, we derive a matrix-based descriptor to represent the protein sequence.

From this distance matrix we derive the basal branching pattern of the chlorophycean subclades using neighbor-joining.

Using the covariance matrix, we derived in (69), and invoking Lemma 8 in [22], we can upper bound (82) as follows: frac{R_{us,2}}{W_{m}}leq text{log}left|I_{N_{text{ul}}}+bar{lambda}rho_{text{ul}}H_{text{ul}}left(I_{M_{text{ul}}}+bar{lambda}rho_{mathrm{I}}H_{mathrm{I}}^{dagger} H_{mathrm{I}}right)^{-1}H_{text{ul}}^{dagger}right|.

From the estimated M-matrix, we derived the relative change in R0 as outlined in the methods section.

The Drosophila empirical rate matrix we derived using this method is very similar to that reported by Petrov and Hartl [ 51].

In numerical analysis it is often necessary to estimate the condition number CN(T)="‖T‖⋅‖T−1‖ and the norm of the resolvent ∥∥(ζ−T −1∥∥ of a given n×n matrix T. We derive new spectral estimates for these quantities and compute explicit matrices that achieve our bounds.

Utilizing the Fourier transform and propagator matrix method, we derive the induced field quantities in terms of the Stroh formalism.