ternion's Usage Examples:

When Su o, (I + 2wu) () (1 + zwu) -1 is an operator which shifts (without further change) the tri - quaternion operand an amount given by u in direction and distance.

With this notation the values of x and y may be expressed in the forms x q q /N q ', gg /Nq', which are free from ambiguity, since scalars are commutative with quaternions.

The equations q'+x q and y+q' q are satisfied by the same quaternion, which is denoted by q - q'.

gage field theory is more naturally quantised using quaternion Hilbert space, H.

In addition to his political pamphlets Pourquoi et comment je suis Boulangiste (1887) and L'Anarchie bourgeoise (1887), he published mathematical works, among them Introduction a l'etude des quarternions (1881) and Theorie et applications des equipollences (1887).

As will be seen later, the fundamental i, j, k of quarternions, with their reciprocals, furnish a set of six quantities which satisfy the conditions imposed by Servois.

- There are three fairly wellmarked stages of development in quaternions as a geometrical method.

Thus e 1 e 2 - e2ei, and if q, q are any two quaternions, qq is generally different from q'q.

Shaw, in America, independently of Joly, has interpreted the quaternion as a point-symbol.

"These may be compared and contrasted with such quaternion formulae as S(VabVcd) SadSbc-SacSbd dSabc aSbcd - bScda+cSadb where a, b, c, d denote arbitrary vectors.

Quaternions (as a mathematical method) is an extension, or improvement, of Cartesian geometry, in which the artifices of co-ordinate axes, 'c.

(Note that the z here occurring is only required to ensure harmony with tri-quaternions of which our present biquaternions, as also octonions, are particular cases.

This applies also to quaternions, but not to extensive quantities, nor is it true for linear algebras in general.

Synonyms:

3, triplet, terzetto, trinity, trio, III, tierce, tercet, trine, deuce-ace, digit, ternary, leash, triad, trey, troika, three, threesome, figure,

Antonyms:

ordinal, single, untie, integrate, differentiate,