My Math Forum  

Go Back   My Math Forum > College Math Forum > Real Analysis

Real Analysis Real Analysis Math Forum


Reply
 
LinkBack Thread Tools Display Modes
October 11th, 2011, 04:04 AM   #1
Member
 
Joined: Jan 2010

Posts: 44
Thanks: 0

scalar multiplication axioms

Scalar multiplication is defined generally as a function ,where , - linear space, for which 5 axioms are true:



It is neccessary for any function that defines scalar multiplication, that all of these axioms are true.
I've noticed that some sources offer just 4 axioms - the first and the second is joined into one. Does it mean that the first and the second axiom is equivalent?
If not, then there must be a function for which the first axiom is false, but the remaining ones is true. But I cannot think of such an example.
waytogo is offline  
 
October 16th, 2011, 12:30 AM   #2
Site Founder
 
julien's Avatar
 
Joined: Nov 2006
From: France

Posts: 824
Thanks: 7

Re: scalar multiplication axioms

The first and second axioms are not equivalent, but the two of them can be seen as equivalent to a jointed one:



I let you prove that this axiom can indeed substitute 1 + 2.
julien is offline  
Reply

  My Math Forum > College Math Forum > Real Analysis

Tags
axioms, multiplication, scalar



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
An example of a model that satisfies the axioms of ZFC? sunvogue Applied Math 1 May 6th, 2012 11:33 AM
A Question Regarding Separation Axioms Hooman Real Analysis 5 November 29th, 2011 04:38 AM
Scalar IVP existence-uniqueness for x(t)? lu5t Abstract Algebra 0 March 4th, 2011 08:16 AM
Two axioms mathematics kumarevo Algebra 2 February 23rd, 2011 09:22 AM
Scalar Multiplication in a complex vector Space Teddy Linear Algebra 3 December 11th, 2009 03:08 PM





Copyright © 2019 My Math Forum. All rights reserved.