Sentence examples for matrices and linear from inspiring English sources

We denote matrices and linear spaces with bold uppercase letters and vectors with bold lowercase letters.

In the derivation of the bounds, one only needs to deal with eigenvalues of matrices and linear matrix inequalities, and thus avoids solving high-order algebraic equations.

The relaxed problem is convex and belongs to the class of SDP, as it is composed of cones of positive semdefinite matrices and linear matrix inequalities involving W. The numerical solution can be found by using SDP solvers.

Under the 1-to-1 correspondence between matrices and linear maps, matrix multiplication corresponds to composition of maps: if a k-by-m matrix B represents another linear map g Rm → Rk, then the composition g ∘ f is represented by BA since :(g ∘ f)('x') = g(f('x')) = g(Ax) = B(Ax) = (BA)'x'x

The physics background, matrix and linear envelope-code computations, and particle-in-cell simulations of beam transport over a long propagation distance in UMER are presented.

First we present a methodology for using a combination of computer assistance and human intervention to discover highly algebraic theorems in operator, matrix, and linear systems engineering theory.

A novel polymeric electrolyte system has been developed using oligo ethylene oxide -grafted poxide -graftede matrix and linear polymethacrylatedissolves matrixium sands.

Similarly, if the Eigen matrix and linear algebra library is not found, any classes that require fast matrix manipulation (such as OBAlign, which performs least squares alignment) will not be compiled.

Essentially, the steps of the term-order-free reverse engineering comprise standard matrix and linear algebra calculations.

For example, the first column (x1) (K-lignin column) showed the scatter plots of other nine variables (xi, i = 2-9) as listed in each row in the diagonal versus K-lignin content with ellipse matrix and linear fit with the adjusted R-square to investigate the correlations.

In [12], under some suitable assumptions, utilizing a matrix decomposition and linear matrix inequality (LMI) method, the authors have proposed some the new global asymptotic stability sufficient conditions for RDNNs with continuously distributed delays.