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Bernhardsson, Bo and Cobos, Fernando and Kühn, Tomas and Mondoc, Daniel and Peetre, Jaak
(2006)
*Quaternary binary trilinear forms of norm unity.*
Proceedings of the Estonian Academy of Sciences, 55
(3).
pp. 150-158.
ISSN 1736-6046

PDF
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Official URL: http://www.kirj.ee/public/va_fm/phys-2006-3-4.pdf

## Abstract

So far trilinear forms have mostly been considered in low dimensions, in particular the dimension two (binary) case, and when the ring of scalars K is either the real numbers R

or the complex ones C. The main aim in both situations has been to decide when a normalized form has norm unity. Here we consider the case of quaternions, K = H. This note is rather preliminary, and somewhat experimental, where the computer program Mathematica plays a certain role. A preliminary result obtained is that the form has norm unity if and only if the discriminant of a certain 5-dimensional quadratic form has all its principal minors nonnegative.

We found also a rather unexpected similarity between the noncommutative case of Hnand the commutative one of R and C.

Item Type: | Article |
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Uncontrolled Keywords: | Trilinear form; quaternion; discriminant; principal minor |

Subjects: | Sciences > Mathematics > Numerical analysis |

ID Code: | 22394 |

Deposited On: | 16 Jul 2013 10:11 |

Last Modified: | 06 Aug 2018 11:26 |

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