Abstract
The invariants of a pair of quadratic forms and a pair of coplanar conics are revisited following [1, 5, 2]. For a given pair of conies, with their associated matrices C1 and C2, we show that Trace (C-12C1), Trace (C-11C2) and ∣C1∣/∣C1∣ are only invariants of associated quadratic forms, but not invariants of the conies. Two of true invariants of the conies are \(\frac{{Trace(C_2^{ - 1} C_1 )}}{{(Trace(C_2^{ - 1} C_1 ))^2 }}\frac{{\left| {C_2 } \right|}}{{\left| {C_1 } \right|}}and\frac{{Trace(C_2^{ - 1} C_1 )}}{{(Trace(C_2^{ - 1} C_1 ))^2 }}\frac{{\left| {C_1 } \right|}}{{\left| {C_2 } \right|}}\). Then the true invariants of the conies are geometrically interpreted, in terms of cross ratios, through the common self-polar triangle of the two conies.
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© 1991 Springer-Verlag London Limited
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Quan, L., Gros, P., Mohr, R. (1991). Invariants of a Pair of Conics Revisited. In: Mowforth, P. (eds) BMVC91. Springer, London. https://doi.org/10.1007/978-1-4471-1921-0_10
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DOI: https://doi.org/10.1007/978-1-4471-1921-0_10
Publisher Name: Springer, London
Print ISBN: 978-3-540-19715-7
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