
#1
Nov1312, 11:20 PM

P: 391

Hi, Algebraists:
Say V is finitedimensional over F . Is there more than one way of defining the action of F on V (of course, satisfying the vector space axioms.) By different ways, I mean that the two actions are not equivariant. Thanks. 



#2
Nov1412, 04:19 PM

P: 302

But in general, there can be more than one possibility. For example, If V is a vector space over C (the complex numbers), and if a' denotes the conjugate of a complex number a, then we define a new action x of C upon V by a x v = a'v (where a'v is computed by the original action). It can be shown that V with this new action and the same addition as before satisfies the vector space axioms. 


Register to reply 
Related Discussions  
Is the Field of Reals in and of itself a Vector Space?  Linear & Abstract Algebra  3  
Vector space over field F  Linear & Abstract Algebra  10  
vector space vs field  Calculus & Beyond Homework  3  
sO(n) actions on vector bundles  Differential Geometry  3  
Vector Space over field of R  Introductory Physics Homework  2 