Sentence examples for matrices and therefore from inspiring English sources

N1, N2 are full rank matrices and therefore have inverse matrices, as proved in Appendix.

Naive discretisation leads to full matrices and therefore to quadratic complexity O(n2), if n denotes the number of degrees of freedom.

For instance, if the full matrix is used, the computation of in (8) involves full matrices, and therefore the computational complexity would be at least.

Since the access pattern is strongly dependent on the distortion parameters and homography matrices and therefore not incremental in general, the effective available bandwidth of DRAM components is severely degraded and clearly insufficient to support the desired frame rates.

So changing (I^{c}) can transform real eigenvalues into imaginary ones (in non-symmetric connectivity matrices) and therefore generate oscillations, or change the sign of the real part of an eigenvalue from negative to positive, giving rise to an instability.

A low value of coherence between Φ m and the basis where the signal becomes sparse (Fourier in our case) is desirable in order to ensure mutually independent matrices and therefore better compressive sampling.

Then, for any diagonal matrix P, whose diagonals are zeros or ones, the two matrices (I- P + AP) and (I-P + PA) are M-matrices, and therefore, ((I- P + AP)^{-1}geq0) and ((I- P + PA)^{-1}geq0).

In each case, different concentration profiles develop within the porous matrix and, therefore, distinct optimal conditions are expected.

Phonon propagation speed is a function of the mechanical properties of the matrix and therefore a function of hydrogen content.

Since its off-diagonal entries are all nonpositive, the matrix must be a Stieltjes matrix and therefore an M-matrix [23].

Furthermore, the crystalline phases are shown to be harder than the glassy matrix, and therefore likely contribute to the high wear-resistance of the studied BMG.