Sentence examples for matrix and hence from inspiring English sources

Those weaken the matrix and hence reduce the split strength of concrete.

Here, (mathbf {H}^{mathcal {H}} mathbf {H}) is a full-rank N×N matrix and hence always invertible.

Note that changing θ only affects the cross-covariance matrix, and hence has no effect on the best achievable rates for independent coding of the two sources.

This is to note that the proposed Optshrink LR + S method estimates a denoised version of low-rank matrix and hence yields better results.

Consequently, each term in the infinite series expressing A is a Hermitean matrix, and hence this matrix is Hermitean as well.

This means that if the successive regressors are orthogonal, we can simply replace P i with an identity matrix and hence discard Equation 25.

Fibers of carbon or graphite are known to be inert with the matrices and hence possibility of composites with weaker interface always exists.

One can notice from (10) that matrices A k and B k are written as the sum of semi-definite positive matrices and hence are positive semi-definite.

Most of finite element model updating techniques do not employ damping matrices and hence, cannot be used for accurate prediction of complex frequency response functions (FRFs).

The application of the matching method to the identification of unknown system matrices, and hence to shifting a system resonance frequency, is presented.

This is because X1 and X2 have different auto-covariance matrices, and hence inter-changing the rates is equivalent to inter-changing the terminals.