Sentence examples for matrices are expanded from inspiring English sources

Using the KL expansion, the mass and stiffness matrices are expanded in series in terms of discrete parameters.

All elements of an arbitrary density matrix can be reconstructed using the phase kick-back method, if the density matrix is expanded in the product operator basis44.

Upon heating via the hot medium, the PS matrix was expanded to form a cellular structure.

Cells C[0,j] = 0 and cells C[i,0] = i, and next, the matrix is expanded according to the recursive formulas in Eq. (1) [22].

Another benchmark proposed by Kausel and Roesset contributes an alternative, in which the dynamic stiffness matrix is expanded in terms of wave number and approximated by taking terms only up to the second order of the wave number.

The unbiased position specific expectation deviation scoring matrix was expanded into a hyper-dimensional vector representation, and the Euclidean distances between vectors was computed.

Results show that with increasing heat treatment temperature the crystallite size increases, the degree of order is improved, the thickness of laminar graphite around the carbon fibers increases, and the number of interfacial cracks between the fiber and matrix decrease and cracks between matrix layers are expanded.

In both perturbation methods, the subinterval matrix and vector are expanded by the Taylor series.

In both FSPFEM and MSPFEM, the subinterval matrix and vector are expanded by the Taylor series.

The interval matrix and vector are expanded by the modified Taylor series.

In the proposed method, the interval random matrix and vector are expanded by the first-order Taylor series and the sound pressure response vector is obtained by the matrix perturbation technique.