No CrossRef data available.
Article contents
3. Note on the Reality of the Roots of the Symbolical Cubic which expresses the Properties of a Self-conjugate Linear and Vector Function
Published online by Cambridge University Press: 15 September 2014
Extract
Hamilton has shown that if
where α and β are given vectors, and A a given scalar, we have
where m, m1, m2, are scalars depending only on φ.
When the function φ is its own conjugate, i.e., when
ρ and σ being any vectors whatever, the vectors for which
form in general a real and definite rectangular system. This, of course, may in particular cases degrade into one definite vector, and any pair of others perpendicular to it; and cases may occur in which the equation is satisfied for every vector.
- Type
- Proceedings 1866-67
- Information
- Copyright
- Copyright © Royal Society of Edinburgh 1869