# 反对称和正交矩阵

 In[1]:= XaSimple[t_] = {{0, 1, 2}, {-1, 0, 3}, {-2, -3, 0}};
 In[2]:= XAntisymmetricMatrixQ[aSimple[t]]
 Out[2]=

 In[3]:= Xu[t_] = MatrixExp[aSimple[t] t];
 In[4]:= XvSimple[t_] := u[t] . {vx, vy, vz};

 In[5]:= XvSimple'[t] == aSimple[t].vSimple[t] // Simplify
 Out[5]=

 In[6]:= XOrthogonalMatrixQ[u[t]]
 Out[6]=

 In[7]:= XBlock[{vx = 0, vy = 0, vz = 1}, Show[ParametricPlot3D[vSimple[t], {t, 0, 10}, Lighting -> "Neutral", ColorFunction -> (ColorData["Rainbow"][#4] &)], Graphics3D[{Opacity[.5], Sphere[]}], PlotRange -> All, ImageSize -> Medium]]
 Out[7]=

 In[8]:= XaComplex[t_] := {{0, -t + Sin[t], -Cos[t/2]}, {t - Sin[t], 0, t Cos[t]}, {Cos[t/2], -t Cos[t], 0}}
 In[9]:= XAntisymmetricMatrixQ[aComplex[t]]
 Out[9]=

 In[10]:= XvComplex = NDSolveValue[{v'[t] == aComplex[t].v[t], v[0] == {1, 0, 0}}, v, {t, 0, 10}];
 In[11]:= XShow[ParametricPlot3D[vComplex[t], {t, 0, 10}, Lighting -> "Neutral", ColorFunction -> (ColorData["Rainbow"][#4] &)], Graphics3D[{Opacity[.5], Sphere[]}], PlotRange -> All, ImageSize -> Medium]
 Out[11]=

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