Sentence examples for matrices need not from inspiring English sources

New element matrices need not be generated and the singular numerical integration was avoided completely.

New element matrices need not be generated and integration is avoided completely.

From conditions (9) in Theorem 2 it is clear that some constants with respect to the neuron activation functions and coefficient matrices need not be known beforehand.

Further, an adaptive strategy is introduced to design adaptive feedback controllers, where some constants with respect to system parameters including node dynamics and coupling matrices need not be calculated beforehand.

Since the domain repertoire in the human proteome is an incremental collection along its evolutionary lineage, soft matrices need not always be effective in finding all homologs.

In contrast to previous results, the coupling configuration matrix needs not be symmetric or irreducible.

Unlike traditional randomized gossip algorithms, push-sum mechanism based BMGA preserves the sums and weights, and admits stochastic diffusion matrices which need not be doubly stochastic.

In addition, different from [12, 21], the inner-coupling matrix Γ need not to be a diagonal matrix in this paper.

Particularly, the weight configuration matrix is not necessarily symmetric or irreducible, and the inner coupling matrix need not be symmetric.

Moreover, the constant term (center) of the uncertain time-varying state matrix need not be diagonalizable thanks to results based on a Jordan decomposition.

Depending on the numbers of rows and columns, the requirements for optimality can be decidedly counterintuitive: replication numbers need not be as equal as possible, and trace of the information matrix need not be maximal.