Sentence examples for matrices are both from inspiring English sources

Let us prove, for these four matrices above, that the second matrix is positive definite while the third and/or the fourth matrices are both negative definite.

Since the precoding matrices are both constructed, we can rewrite the observation at the i th user as y i = α R | h i | 2 ( α B s i + x i ) + α R h i H n R + n i, (15).

The two matrices were both analyzed using the software package TNT [15], with the implicit enumeration search strategy.

Expansion of the matrix chains is seen when the particles and matrix are both represented by a small number of beads, but contraction of matrix chains can be observed when both species contain a large number of beads.

A three-dimensional nanoscale cylindrical representative volume element (RVE) has been considered in the analysis, in which CNT and matrix are both modeled as elastic materials based on continuum mechanics.

Cell spreading and integrin-based adhesion to the extracellular matrix are both known to require activation of Rho GTPases that would effect the analysis of Rac1 in whole cell assays [25], [26].

If a matrix is both positive semidefinite and centrosymmetric, we call this matrix positive semidefinite centrosymmetric.

This bandwidth matrix is both positive and definite, important because the matrix must have a square root.

Fibrils and matrix were both defined as isotropic linear elastic materials with a Poisson's ratio of 0.3.

Digestion of extracellular matrix is both a major event during cell invasion and an indication of aggressive properties of cancer cells.

Many examples of optimal correlation matrices are given, both analytically and numerically.