quaternions's Usage Examples:

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.

- 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.

(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.

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.

Thus every quaternion may be written in the form q Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.

Here the symmetry points at once to the selection of the three principal axes as the directions for i, j, k; and it would appear at first sight as if quaternions could not simplify, though they might improve in elegance, the solution of questions of this kind.

The chief defect of the geometrical properties of these bi-quaternions is that the ordinary algebraic scalar finds no place among them, and in consequence Q:1 is meaningless.

His earliest work dealt mainly with mathematical subjects, and especially with quaternions (q.

3 And now the product of two quaternions could be at once expressed as a third quaternion, thus (a+ib+jc+kd) (a'+ib'+jc'+kd') A+iB+jC+kD, where Aaa' - bb' - cc' - dd', B ab'+ba'+cd' - dc', C ac'+ca'+db' - bd', D ad' +da'+bc' - cb'.

Various special algebras (for example, quaternions) may be expressed in the notation of the algebra of matrices.

Synonyms:

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

Antonyms:

differentiate, integrate, single, cardinal, ordinal,