Vector subtraction is performed by adding the scalar multiple of " 1 with the second vector operand to the first vector operand.
12.
Elements of the geometric algebra that are simply scalar multiples of 1 are grade-0 blades and are called " scalars ".
13.
An algebra is " central " if its centroid consists of the " K "-scalar multiples of the identity.
14.
By Schur's lemma and the Gelfand Naimark construction, the matrix coefficient of any vector determines the vector up to a scalar multiple.
15.
If "'F "'is algebraically closed, the only equivariant endomorphisms of an irreducible representation are the scalar multiples of the identity.
16.
We shall show that " I " must be equal to by proving that it contains a nonzero scalar multiple of " ? ".
17.
The non-zero scalar multiples, written as coordinate triples, are the homogeneous coordinates of the given point, called " point coordinates ".
18.
This line may be denoted by " line coordinates " which are also homogeneous coordinates since non-zero scalar multiples would give the same line.
19.
In other words, the only linear transformations of " M " that commute with all transformations coming from " R " are scalar multiples of the identity.
20.
Since the second term in y _ 2 ( x ) is a scalar multiple of the first solution ( and thus linearly dependent ) we can drop that term, yielding a final solution of
