Abstract
We have determined the volume of parallelotopes in Euclidean space with the aid of determinants in Proposition 3.4. In this chapter we present a far-reaching generalization of this issue which dates back to Jacobi.
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Notes
- 1.
Carl Gustav Jacobi, 1804–1851, born in Potsdam, active in Königsberg and Berlin. He worked in number theory, elliptic functions, and mechanics.
- 2.
Carl Friedrich Gauss, 1777–1855, born in Braunschweig, active in Braunschweig and at the observatory in Göttingen. His contributions shape the whole of mathematics until the present time. For astronomy, physics and geodesy, too, he has lasting merits.
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Brokate, M., Kersting, G. (2015). The Jacobi Transformation Formula. In: Measure and Integral. Compact Textbooks in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-15365-0_10
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DOI: https://doi.org/10.1007/978-3-319-15365-0_10
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