Tensor of a quaternion
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Hi every body, there needs to be an article on the concept that a quaternion has a tensor. I don't think that this discussion should be limited to only 19th century sources like the article classical hamiltonian quaternions. Clearly this is an idea that moves into the 20th century and evolves.
Hamilton did not, as now claimed, define a tensor to be "a signless number"; what he actually says is:
- it seems convenient to enlarge by definition the signification of the new word tensor, so as to render it capable of including also those other cases in which we operate on a line by diminishing instead of increasing its length ; and generally by altering that length in any definite ratio. We shall thus (as was hinted at the end of the article in question) have fractional and even incommensurable tensors, which will simply be numerical multipliers, and will all be positive or (to speak more properly) SignLess Numbers, that is, unclothed with the algebraical signs of positive and negative ; because, in the operation here considered, we abstract from the directions (as well as from the situations) of the lines which are compared or operated on.