quaternion'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.

- 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.

(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.

The outer and inner products of two extensive quantities A, B, are in many ways analogous to the quaternion symbols Vab and Sab respectively.

In addition, quaternions was one of the themes of his address as president of the mathematical section of the British Association in 1871.

Neither of these men professed to employ the calculus itself, but they recognized fully the extraordinary clearness of insight which is gained even by merely translating the unwieldy Cartesian expressions met with in hydrokinetics and in electrodynamics into the pregnant language of quaternions.

Synonyms:

tetrad, figure, quatern, four, digit, quaternary, quartet, 4, foursome, IV, quaternity, Little Joe, quadruplet,

Antonyms:

differentiate, integrate, single, cardinal, ordinal,