Sentence examples for cross products from inspiring English sources

They represent the linear, quadratic and cross products of x1, x2, x3 on response.

For the same reasons as discussed above, the average values of the cross products between these terms are zero.

Because is expressed in terms of, this search does not require evaluating cross products of different workloads; each workload is only optimized once per value of checked.

This is important because the nonlinear mapping will involve various cross products of components within a vector of the input space.

The other kernels (with p≥2) are nonlinear kernels whose outputs depend on cross products of samples of the input signal.

As an application we give lower and upper estimations for the asphericity of infinite and finite cross products of these sets in certain spaces, respectively.

The kernel does not need to be strictly a matrix of cross-products between the input vectors.

Prior to running the PCA, the elements of each cross-products matrix were "correlated" (centered and standardized by standard deviation) to remove magnitude differences among variables [37].

Due to the presence of unknown cross-products, the addition of a set of auxiliary equation is necessary to solve the problem.

In this case, the linear coefficients X1, X2, X3, and X4; the cross-products, X1X2, X1X3, X1X4, X2X3, X2X4, and X3X4; and the quadratic coefficients, X12, X22, X32, and X42 are significant model terms (Table 3).

The reason is that cross-products such as ( mathrm{I}mathrm{m}left {A}_y^{A}_zright)mathrm{I}mathrm{m}left {B}_y^{B}_zright) ) are harder to handle in the fourth-order polynomials in Eq. (9.3).