 
Summary: 1. Vectors.
In what follows n will always be a positive integer.
A scalar is a real number. An nvector is an ordered ntuple of scalars. When
it is clear from the context what n is we will frequently say "vector" instead of
"nvector". If (x1
, . . . , xn
) is an nvector then, for each i = 1, . . . , n, the scalar xi
is called the ith component of the nvector. (In the book
(x1
, . . . , xn
) is denoted by < x1, . . . , xn > .
Let
Rn
denote the set of vectors.
Given a vector x and a scalar c we let
cx = (cx1
, . . . , cxn
)
be the vector whose ith component is c times the ith component of x, i = 1, . . . , n;
cx is called scalar multiplication of x by c. If c = 0 we will often write
