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Theorem regarding the Orthogonal Transformation of a Quadric

Published online by Cambridge University Press:  15 September 2014

Thomas Muir
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Extract

The theorem in question arises out of a consideration ol several passages in Jacobi's important memoir of 1833 or orthogonal transformation. Having determined the substitutior which simultaneously changes

and

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 25 , Issue 1 , 1906 , pp. 168 - 172
Copyright
Copyright © Royal Society of Edinburgh 1906

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References

note * page 68 Jacobi, C. G. J., De binis qnibuslibet functionibus homogeueis secunc ordinis per substitutiones lineares in alias binas transformandis …. Crelle's Journ., xii. pp. 1–69. (Aug. 1833.)Google Scholar

note * page 169 Traiu. R. S. Edinb., xxxii. p. 480.

note * page 171 Jacobi's enunciation of this is “I n relationibus omnibus, quae inter variabiles x 1, x 2, …, x n, et variabiles y 1, y 2, …, y n locum habent, simul loco y m poni posse , atque loco x λ

where the b's correspond to the modern A's, and the sign of equality is used for ‘or.'