With regard Vector Space Definition?

[ksquare]

Hi,

 

Does one of the conditions for the definition of Vector Space V over a Field F include :

 

1) Closure property in vector addition.

2) Closure property in scalar multiplication.

 

Or are these conditions included only in the definition of Linear Vector Spaces?

 

Clear Skies!

kSqUARe

[ajb]

I am not sure exactly what you are asking, but in the definition of a vector space you require closure under addition and multiplication by a scalar.

 

What is the difference between a linear vector space and a vector space? I think they are the same thing.

 

Morphisms between vector spaces are linear maps.

[shif]

I also think that linear vector space and vector space are the same thing (at least in the usual terminology).