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You could also do something like the following (taking advantage of TransformedField: solidHarmonicS[l_?IntegerQ, m_?IntegerQ, x_, y_, z_] := Module[{r, θ, ϕ, xx, yy, zz}, FullSimplify@ Evaluate[ TransformedField["Spherical" -> "Cartesian", r^l SphericalHarmonicY[l, m, θ, ϕ], {r, θ, ϕ} -> {xx, yy, zz}]] /. {xx -> x, yy ...


2

Your expression simplifies to this $$\vec X \vec X^T A + A^T \vec X \vec X^T$$ using just these rules Unprotect[D, Transpose, Dot]; (*Derivative rules*) D[Tr[A_], X_] := Tr[D[A, X]] D[Transpose[A_], X_] := D[A, X]\[Transpose] D[A_ .B_, X_] := D[A, X].B + A.D[B, X] (*Tranpose rules*) 0\[Transpose] := 0 1\[Transpose] := 1 (A_\[Transpose])\[Transpose] := A ...


1

The matrix Clear[a,B,d,j,M]; m = {{B/2 - d - j/2 + a, (Sqrt[2]*j)/2, M}, {(Sqrt[2]*j)/2, B/2 + a, 0}, {M, 0, (-3*B)/2 - d + j/2 + a}}; has eigenvalues determined by the characteristic polynomial of (maximal) degree 3. In the absence of any other information, we get three Root objects as the eigenvalues, which is Mathematica's way of preserving all ...



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