Confirming in Mathematica: In[45]:= With[{axisVec = {1, 0, 0}}, RotationMatrix[\[Theta], axisVec].(LeviCivitaTensor[3].{Subscript[w, 1], Subscript[w, 2], Subscript[w, 3]}).RotationMatrix[-\[Theta], axisVec] - (LeviCivitaTensor[3].RotationMatrix[\[Theta], axisVec].{Subscrip...
In practice, however, the complex integral operations in Eqs. (3.21) are not necessary. Alternatively, one needs to perform the product-to-sum formula to the integrands of Eqs. (3.21) to obtain the Fourier coefficients (mˆ0,mˆ1,…,mˆ2N). In Mathematica, the harmonic balance proce...
This is easily done using a different form of the sparse function. This time the function is supplied with the location of the non-zero entries in the matrix, the value of these entries, the size of the sparse matrix and the space allocated for the non-zero entries. This function call ...
(*Perform the Tucker decomposition and store the result*)result=ResourceFunction["TuckerDecomposition"][{{{1,2},{3,4}},{{5,6},{7,8}}}];(*Display the result nicely*)Grid[{{"Core Tensor:",MatrixForm[result[[1]]]},{"Factor Matrices:",TableForm[result[[2]]]}},Alignment->Left,Fra...
SuiteSparse has many user-definable settings of the form SUITESPARSE_USE_* or (package)_USE_* for some particular package. In general, these settings are not strict. For example, if SUITESPARSE_USE_OPENMP is ON then OpenMP is preferred, but SuiteSparse can be used without OpenMP so no error...
We are interested in the study of the sum E + F and the product E * F , when E and F are of the form s ξ, or s ξ ° , or s ξ ( c ) . Then we deal with the identities ( E + F )(Δ q ) = E and ( E + F )(Δ q ) = F . Finally we consider matrix ...
The easiest way to generate random boolean matrices, is like this: (* Generate 1 random 3x3 matrix *)RandomChoice[{True,False},{3,3}](* Generate 10 of them *)RandomChoice[{True,False},{10,3,3}] s=m[{1,1,},{]),r},r=Select[sel,tst@&];[]] TableForm[...
When using Mathematica, the routine MatrixExp[, ] gives the result directly in terms of RootSum[, ]. The three diagonal generators are λ3=diag(1,−1,0,0),λ8=diag(1,1,−2,0)/3, and λ15=diag(1,1,1,−3)/6. The remaining 12 generators have two non-zero entries either ...
Although the FID signal sϕ(t) appears in the time domain, it represents the Fourier domain projection data. Therefore, the projection data pϕ(x′) are obtained through the Fourier transform of the FID signal as (56)pϕ(x′)=F[sϕ(t);t→x′]. The basic form of projection ...
Although the FID signal sϕ(t) appears in the time domain, it represents the Fourier domain projection data. Therefore, the projection data pϕ(x′) are obtained through the Fourier transform of the FID signal as (56)pϕ(x′)=F[sϕ(t);t→x′]. The basic form of projection ...