Re: Can we define a vector space over different fields!?
- From: hagman <google@xxxxxxxxxxxxx>
- Date: Mon, 22 Oct 2007 10:31:27 -0700
On 22 Okt., 17:53, m7ossny <m7os...@xxxxxxxxx> wrote:
Hi,
I have a problem where i need to use vector algebra. But vectors'
coordinates are defined with features from different types like real
numbers, rational numbers, functions, or any other abstract type (it
is not always gonna be numbers).
What I can guarantee is that each of these types has its addition/
multiplication/scalar multiplication defined in its own way.
Can I declare a vector space over these fields together RxNxHx...
Thanks alot for time, Bye.
Vector fields are defined over fields (e.g. the field of rational
numbers,
of real numbers, of complex numbers, of meromorphic functions.
You have essentially three options:
a) View everything as a vector space over the rationals (provided
all of your fields are of characteritic zero).
b) Extend everything to a vector space over the biggest of your
fields per tensor products
c) The direct product of your fields is a ring; view your
space as a module over this ring.
hagman
.
- References:
- Can we define a vector space over different fields!?
- From: m7ossny
- Can we define a vector space over different fields!?
- Prev by Date: Re: Factorisation algorithms
- Next by Date: Re: Maximum modulus question 2.
- Previous by thread: Can we define a vector space over different fields!?
- Next by thread: Can we define a vector space over different fields!?
- Index(es):
Relevant Pages
|
