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Vector Space question

by amolv06
Tags: space, vector
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Feb25-08, 06:26 PM
P: 47
1. The problem statement, all variables and given/known data

Let R denote the set of real numbers. Define scalar multiplication by [tex]\alpha x = \alpha x[/tex] which is simply regular scalar multiplication, and vector addition is defined as [tex]x \oplus y = max(x,y)[/tex]. Is R a vector space with these operations?

2. Relevant equations

Some given above.

3. The attempt at a solution

There seems to be no zero vector to this equation as for any number k there exists another number k-1, so there is no single 0 vector for a vector space with the operations defined above. Is this reasoning correct?
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Feb25-08, 08:53 PM
Sci Advisor
PF Gold
P: 39,495
Yes, that's true. So what is your answer to the question?
Feb27-08, 07:16 PM
P: 47
Then it is not a proper vector space!

Thanks a lot.

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