Geodesic
Right and Left Orthogonality
Canadian mathematical bulletin, Tome 4 (1961) no. 2, pp. 182-184

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Let V be a vector space over an arbitrary field F. In V a bilinear form is given. If f is symmetric [(x, y) ≡ (y, x)] or skew-symmetric [(x, y) + (y, x) ≡ 0], then 1 Thus right and left orthogonality coincide. It is well known that (1) implies conversely that f is either symmetric or skew-symmetric in V. We wish to give a simple proof of this result. 
Wild, Jonathan. Right and Left Orthogonality. Canadian mathematical bulletin, Tome 4 (1961) no. 2, pp. 182-184. doi: 10.4153/CMB-1961-021-2
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     title = {Right and {Left} {Orthogonality}},
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     doi = {10.4153/CMB-1961-021-2},
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