- #1
Saladsamurai
- 3,020
- 7
Alrighty then
I am working through Axler's LA Done Right. I have 2 questions for now:
1.) He uses some notation that is confusing me. When referring to [itex]\mathbf{R} \text{ or }\mathbf{C}[/itex] as a set it is in BOLD but when he refers to a vector space as being the set V, it is not in boldface. Why?
2.) I am also a little confused by part of the definition of a Vector Space.
Def: A vector space is a set V along with an addition on V and a scalar multiplication on V such
that the following properties hold: commutativity, associativity, ...etc.
(Here is where I get confused)
He never actually says what this means.
Thanks!
I am working through Axler's LA Done Right. I have 2 questions for now:
1.) He uses some notation that is confusing me. When referring to [itex]\mathbf{R} \text{ or }\mathbf{C}[/itex] as a set it is in BOLD but when he refers to a vector space as being the set V, it is not in boldface. Why?
2.) I am also a little confused by part of the definition of a Vector Space.
Def: A vector space is a set V along with an addition on V and a scalar multiplication on V such
that the following properties hold: commutativity, associativity, ...etc.
(Here is where I get confused)
Can someone clarify what he means by a vector space over F or over R and how that is different from just saying a vector space?The scalar multiplication in a vector space depends upon F (where F can refer to either [itex]\mathbf{R}\text{ or }\mathbf{C}[/itex]). Thus when we need to be precise, we will say that V is a vector space over F instead of simply saying that V is a vector space. For example, Rn is a vector space over R and Cn is a vector space over C.
He never actually says what this means.
Thanks!