The file ratematrix.py contains Python code to calculate the sparse matrix elements of the transition rate matrix for a given Cantera .cti model and find eigenvalues and eigenvectors. The plot.nb file is a Mathematica notebook for plotting results. The folder mechanisms contains a few .cti mode...
{pmatrix}-2\\1\\0\end{pmatrix}$ So for the eigenvalue $\lambda_1=2$ its all eigenvectors are $k_1\xi_1 \ (k_1\neq 0, k_1\in P)$ In a same way, all eigenvalues and eigenvector are $latex(var["A"].eigenvects()) = \left[ \left( 2, \ 1, \ \left[ \left[\...
which involve multiplying two numbers and adding the result. This operation is fundamental to many linear algebra operations, such as matrix multiplications, convolutions, and dot products. MACs are often used as a more specific measure of computational complexity in models that heavily rely on linea...
(Side note: In fact, the two values for xx that we got above, one of which was the golden ratio ϕϕ , are the eigenvalues of the matrix above. So using the matrix equation above and a bit of linear algebra would be yet another way of deriving the closed formula.) All right. ...
PyCrystalField can also fit the crystal field Hamiltonian to data. The user can define an arbitrary ChiSquared function based on any observables (neutron data, susceptibility, magnetization, or eigenvalues) and PyCrystalField will minimize the ChiSquared function by varying a defined set of CEF pa...