Sentence examples for linear operations from inspiring English sources

end{aligned}Since both W and (nabla) are linear operations, we can stack these operators into a single operator to obtain begin{aligned} ||Wx - p ||_2^2 + lambda ^2 ||nabla x ||_2^2 = left|left|left( {begin{array}{c}W lambda nabla end{array}}right) x - left( {begin{array}{c}p 0end{array}}right) right|right|_2^2.

Spatial operations used in image processing are linear operations.

Using phasors, all the light transport events in C-ToF imaging can be represented by linear operations on complex numbers.

This Parameterized Digital Electronic Arithmetic (PDEA) model replaces linear operations with non-linear ones.

Together with ordinary coherence functions, a measured output spectrum for these models can be decomposed into three components representing the linear operations, the non-linear operations, and the remaining uncorrelated noise effects.

Another reason for the success of the complex sinusoid is that we will be concerned only with real linear operations on signals.

The main innovation in this paper is to use a larger set of possible bases to achieve maximum bandedness of linear operations.

Non-linear coherence functions are defined from these models which determine the proportion of the output spectrum due to the non-linear operations.

Increasingly the mechanisms hypothesized involve non-sequential organization of non-linear operations and so exceed the ability of researchers to mentally rehearse their behavior.

The adopted procedure is shown to be fully compatible with the linear analysis, applicable to the case of infinitesimal jumps, and to circumvent the problem of the inadmissibility of non-linear operations in the general jump analysis.

It has been established that a signal in the reconstruction set based on wavelet maximum curvature point representation associated with specified non-linear operations removing insignificant information contains complete information for characterization.