Tensor of a quaternion: Difference between revisions

Revision as of 19:48, 27 March 2009

Revision as of 19:58, 27 March 2009

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{{Expert|date=March 2009}}

=Definition of the tensor of a quaterion=

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==Bitensors==

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If Q is a [[Classical_hamiltonian_quaternions#Biquaternion|biquaternion]] then the operation of taking the tensor of a biquaternion returns a bitensor.<ref>[http://books.google.com/books?id=TCwPAAAAIAAJ&printsec=frontcover&dq=bitensor+biquaternion#PRA1-PA665,M1 Hamilton 1853 pg 655-666 Introduction of the term bitensor in conjunction with biquaternion]</ref>

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=Relation to norm=

{{Expert|section|date=March 2009}}

{{Original research|section|date=March 2009}}

{{dispute|section}}

In [[mathematics]], some thinkers{{Who|date=March 2009}} 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.

{{synthesis|section}}

In [[mathematics]], some thinkers{{Who|date=March<ref>Hamilton, 2009}}Tait, Cayley, Hardy, and all the modern thinkers agree there is some type of relationship, but they differ on the nature of this relationship.</ref> 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.

Hamilton did not, as now claimed, ''define'' a tensor to be "a signless number"; what he actually says is: