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=Applications=
==Stresses and Strains==
Since the tensor of a quaternion represents its stretching factor one of its many applications is in the computations of stresses and strains.<ref>[http://books.google.com/books?id=CGZLAAAAMAAJ&pg=PA146&dq=homogeneous+strain+deformable#PPA294,M1 See Tait section on stresses and strains]</ref>
=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.
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