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1. Vectors. In what follows n will always be a positive integer.
 

Summary: 1. Vectors.
In what follows n will always be a positive integer.
A scalar is a real number. An n-vector is an ordered n-tuple of scalars. When
it is clear from the context what n is we will frequently say "vector" instead of
"n-vector". If (x1
, . . . , xn
) is an n-vector then, for each i = 1, . . . , n, the scalar xi
is called the i-th component of the n-vector. (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 i-th component is c times the i-th component of x, i = 1, . . . , n;
cx is called scalar multiplication of x by c. If c = 0 we will often write

  

Source: Allard, William K. - Department of Mathematics, Duke University

 

Collections: Mathematics