Page 83 - 35Linear Algebra
P. 83
4
Vectors in Space, n-Vectors
To continue our linear algebra journey, we must discuss n-vectors with an
arbitrarily large number of components. The simplest way to think about
these is as ordered lists of numbers,
a 1
.
a = . .
.
a n
Do not be confused by our use of a superscript to label components of a vector.
2
Here a denotes the second component of the vector a, rather than the number
a squared!
We emphasize that order matters:
Example 43 (Order of Components Matters)
7 7
4
2
6= .
2 4
5 5
n
The set of all n-vectors is denoted R . As an equation
a 1
n
.
R := . 1 n .
. a , . . . , a ∈ R
a
n
83
