Tensor of a quaternion: Difference between revisions

Revision as of 18:39, 26 March 2009

Revision as of 19:03, 26 March 2009

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{{Expert|date=March 2009}}

=Definition of the tensor of a quaterion=

In the nomenclature of [[classical hamiltonian quaternions|Hamiltons quaternion calculus]], the word tensor can be used in two different but related contexts. The first context is as an operator, as in take the tensor of something, and the second context is as a positive or more correctly unsigned number.

=Applications=

==Stresses and Strains==

=Relation to norm=

In [[mathematics]], some thinkers{{who}} believe there is a relationship between the norm of a [[Classical Hamiltonian quaternions|quaternion]] and the [[tensor]] of a quaternion. Some writers<ref>[[Quaternion#Conjugation.2C_the_norm.2C_and_division|modern thinkers, see proper section of main article]]</ref> define the norm of a quaternion as having the same formula as the tensor of a quaternion, while other writers<ref>Hamilton, Tait, Cayley</ref> define the norm of a quaternion as the square of the tensor. Hamilton uses the term tensor in two different sences as a [[Classical_Hamiltonian_quaternions#Tensor|positive numerical quantity]] and as an operator that operates on other mathematical entities extracting a tensor quantity from them.