# Scalars Sentence Examples

scalars
• 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.