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Can anybody please provide me some references where to read the complete passages / proofs about how and why the matricial representation of conics and quadrics are useful and they work?

I mean, the theory is rather simple. We can classify conics by looking at the three invariants. Where can I learn how all of this is born?

Thank you!

P.s. Before anyone says it: wikipedia's references are not useful/enough.

Heidegger
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  • If you want the history, go to science history! – trula Jul 18 '22 at 19:57
  • @trula Sorry, not exactly the history. I meant the proof, or a detailed explanation with the passages. – Heidegger Jul 18 '22 at 20:01
  • See, for instance, this recent answer of mine, which gives the equation of a conic based on the focus-directrix definition and a few geometric parameters. Multiplying equation $(2)$ by an unspecified constant $k$ gives the generic second-degree equation. You can substitute the resulting coefficients into results you're seeing (say, on Wikipedia) to confirm their validity. – Blue Jul 18 '22 at 21:42
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    Try chapter 9 of Richter-Gebert Perspectives on Projective Geometry – brainjam Jul 21 '22 at 14:48

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