Geodesic
On a Normal Form of the Orthogonal Transformation III
Canadian mathematical bulletin, Tome 1 (1958) no. 3, pp. 183-191

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Under the assumptions of case of theorem 1 we derive from (3.32) the matrix equation so that there corresponds the matrix B to the bilinear form 4.1 on the linear space 4.2 and fP,μ, is symmetric if ɛ = (-1)μ+1, anti-symmetric if ɛ = (-1)μ.The last statement remains true in the case a) if P is symmetric irreducible because in that case fP,μ is 0. 
Zassenhaus, Hans. On a Normal Form of the Orthogonal Transformation III. Canadian mathematical bulletin, Tome 1 (1958) no. 3, pp. 183-191. doi: 10.4153/CMB-1958-021-6
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     title = {On a {Normal} {Form} of the {Orthogonal} {Transformation} {III}},
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     doi = {10.4153/CMB-1958-021-6},
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