Geodesic
On the Gram Matrix
Canadian mathematical bulletin, Tome 5 (1962) no. 3, pp. 265-280

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The material sketched here is mostly well known and concerns the geometrical inter-relations of vectors in a Hilbert (that is, complete inner product) space. The discussion and references are (obviously) not exhaustive but I hope the reader will find here some interesting problems.We shall permit the scalars to be real, complex or quaternionic numbers. The inner product of vectors x and y will be denoted (x|y). 
Halperin, Israel. On the Gram Matrix. Canadian mathematical bulletin, Tome 5 (1962) no. 3, pp. 265-280. doi: 10.4153/CMB-1962-027-1
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     title = {On the {Gram} {Matrix}},
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     doi = {10.4153/CMB-1962-027-1},
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