Chapter 3---Section 1
Examples and Definition
Chapter 3 Vector Spaces
The operations of addition and scalar multiplication are used in many
diverse
contexts
in
mathematics.
Regardless
of
the
context,
however,
these
operations
usually
obey
the
same
set
of
algebraic
rules.
Thus
a
general
theory
of
mathematical
systems
involving
addition
and
scalar
multiplication will have applications to many areas in mathematics.
搂
1. Examples and Definition
New words and phrases
Vector space
鍚戦噺绌洪棿
Polynomial
澶氶」寮?/p>
Degree
娆℃暟
Axiom
鍏悊
Additive inverse
鍔犳硶閫?/p>
1.1 Examples
Examining the following sets:
(1) V=
2
R
: The set of all vectors
1
2
x
x
飪?/p>
飪?
飪?/p>
飪?/p>
飪?/p>
飪?
(2) V=
m
n
R
飩?/p>
: The set of all mxn matrices
(3) V=
[
,
]
a
b
C
: The set of all continuous functions on the interval
[
,
]
a
b
(4) V=
n
P
: The set of all polynomials of degree less than n.
Question 1: What do they have in common?