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Dec 6, 2023 at 14:23 history became hot network question
Dec 6, 2023 at 13:46 vote accept Tran Khanh
Dec 6, 2023 at 9:00 comment added njuffa Erhard Schmidt, "Zur Theorie der linearen und nichtlinearen Integralgleichungen. I. Teil: Entwicklung willkürlicher Functionen nach System vorgeschriebener." Mathematische Annalen, Vol. 63, No. 4, Mar. 1907, pp. 433-476. Most of the material in this publication originates in Schmidt's 1905 Ph.D. dissertation at the University of Göttingen. Of particular interest appears to be "§ 3. Ersetzung linear unabhängiger Funktionensysteme durch orthogonale" starting on p. 442.
Dec 6, 2023 at 8:58 comment added njuffa FWIW, various commentators opine that the procedure was actually invented by Laplace and already used by Cauchy. J. P. Gram, "Ueber die Entwicklung reeller Functionen in Reihen mittelst der Methode der kleinsten Quadrate." Journal für die reine und angewandte Mathematik, Vol. 94, No. 1, 1883, pp. 41-73. This publication is based in parts on Gram's 1879 Ph.D. thesis (in Danish) at the University of Copenhagen.
Dec 6, 2023 at 8:27 history edited Conifold CC BY-SA 4.0
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