
Real Analysis Real Analysis Math Forum 
 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. 
October 16th, 2011, 12:30 AM  #2 
Site Founder 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. 

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 existenceuniqueness 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 