ABSTRACT
In any problem that we wish to solve, the goal is to find a particular object, chosen from among a large collection of contenders, which satisfies the governing constraints of the problem. The collection of contending objects is often a vector space, and although individual elements of the set can be called by many different names, it is common to call them vectors. Not every set of objects constitutes a vector space. To be specific, if we have a collection of objects 5, we must first define addition and scalar multiplication for these objects. The operations of addition and scalar multiplication are defined to satisfy the usual properties: If x,y,z ∈ S, then
x + y = y + x (commutative law)
x + (y + z) = (x + y) + z (associative law)
0 ∈ S+ x = x (additive identity)
−x ∈ S, −x + x = 0 (additive inverse)
