13-Nov-14

1

Axioms

REAL VECTOR SPACE

Let = , : + = Does V satisfy A1?

A1: +

Let = , such that + = Let = , such that + =

+ = , + , = + , +

+ + + = + + + = + =

V satisfy A1

requires 2 vectors

defines 2 vectors

check the condition of V

13-Nov-14

2

Let = , : + =

Does V satisfy A6?

A6:

Let = , such that + =

= , = ,

+ = + = =

V satisfy A6

requires only 1 vector

defines 1 vector

check the condition of V

Let =

: + =

Does V satisfy A1?

A1: + +

Let =

such that + = .

Let =

such that + = .

requires 2 vectors (matrices)

defines 2 matrices

13-Nov-14

3

+ =

+

= + + + + + +

+ + + = + + + = + =

V satisfy A1

check the condition of V

Let =

: + =

Does V satisfy A6?

A6:

Let =

such that + = .

requires only 1 vector (matrix)

defines 1 matrix

13-Nov-14

4

=

=

+ = + = =

V satisfy A6

check the condition of V

Let = + + + =

Does V satisfy A1?

A1: + + ()

Let = + + such that + =

Let = + + such that + =

+ = + + +

+ + = +

+ + + +

requires 2 vectors(2 set of polynomials)

defines 2 set of polynomials

13-Nov-14

5

+ = + + +

+ + = +

+ + + +

+ + + = + + + = +

V satisfy A1

check the condition of V

Let = + + + =

Does V satisfy A6?

A6:

Let = + + such that + =

= + + =

+ +

+ = + = =

V satisfy A6

requires only 1 vector (1 set of polynomials)

defines 1 set of polynomial

check the condition of V