Sentence examples for matrix is necessary from inspiring English sources

Because these two models are located in different coordinate systems, an optimal spatial transformation matrix is necessary.

In this study we addressed whether urothelium in conjunction with an acellular bladder matrix is necessary for the recruitment of host cells to repopulate the graft and whether the urothelium facilitates trans-differentiation of host fibroblastic cells into bladder smooth muscle type cells.

Consequently, the unitary transformation matrix is necessary for each relay terminal in the training section.

A re-estimation of the pitch of each note based on the updated template matrix is necessary because all templates, as well as pitches, can vary by frame.

However, in this case a preliminary normalizing step of the correlation matrix is necessary [47].

Therefore, the problem is not an issue here because no inverse matrix is necessary.

Positive semidefiniteness, recursiveness, and the variety condition of a moment matrix are necessary and sufficient conditions to solve the quadratic and quartic moment problems.

Supporting chemicals or matrix are necessary for the maintenance of pluripotency in culture, as exemplified in the reliance on fibroblasts and serum in primary studies describing ES cells, EC cells and EG cells, suggesting a non-cell autonomous mechanism in self-renewal.

Moreover, no assumption on the symmetry of the connection matrices is necessary.

The activation functions are not assumed to be differentiable or strictly increasing, and no assumption on the symmetry of the connection matrices is necessary.

For a multi-degree-of-freedom (MDOF) problem with a lumped mass matrix, no factorization or explicit inversion of global matrices is necessary.