Scalars sentence example
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.
To fix a weighted point and a weighted plane in Euclidean space we require 8 scalars, and not the 12 scalars of a tri-quaternion.
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.
This idea finds fuller expression in the algebra of matrices, as to which it must suffice to say that a matrix is a symbol consisting of a rectangular array of scalars, and that matrices may be combined by a rule of addition which obeys the usual laws, and a rule of multiplication which is distributive and associative, but not, in general, commutative.
Combebiac's tri-quaternions, which require the addition of quasi-scalars, independent of one another and of true scalars, and analogous to true scalars.Advertisement
The axis of the member xQ+x'Q' of the second-order complex Q, Q' (where Q=nq+wr, Q'=nq'+wr' and x, x' are scalars) is parallel to a fixed plane and intersects a fixed transversal, viz.
This sort of multiplication is given a special name; it is scalar multiplication, because the numbers are sometimes called scalars.