# Scalars Sentence Examples

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.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.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**.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**.