Sentence examples for by simple linear algebra from inspiring English sources
In the case where the local optimum for P L = 0, it can be easily shown by simple linear algebra that the gradients corresponding to these two (P L = 0 and the average power constraint) active inequality constraints satisfy the linear independence condition.
Simple linear algebra shows that (dF phi)) must be a rotation matrix, i.e. that (operatorname{Fix}(langle mathbf {R}^{mathbf{o}}rangle)) is composed of nodes/foci.
However, we can avoid the calculation of true eigenvalues and eigenfunctions by means of the Rayleigh-Ritz (RR) method, which is a procedure for numerically solving operator equations involving only elementary calculus and simple linear algebra (see [31, 35] for a detailed study about the practical application of the RR method).
This relation also follows from simple linear algebra.
Last but not least, the approaches we introduce here only rely on simple linear algebra and are hence far easier to implement than their classical alternatives.
In the case where R admits a diagonal form, simple linear algebra could help to cut off the computations and answer yes to this question.
Relationships between continuous variables were examined by simple linear regression.
Relationships between variables were determined by simple linear regression analysis.
The mathematical content of the modules is appropriate for a variety of mathematics courses (in increasing level of difficulty) outside of the calculus-based sequences, including discrete mathematics, elementary linear algebra, elementary probability, applied matrix algebra, mathematical modeling, linear algebra, computational algebra and algebraic geometry, abstract algebra, and others.
