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adunb8
Group Title
linear algebra question
I know what R^3 or R^2 or R is but what is F, F^infinite and F1, F2, F3 ?? stuff like that i dont understand
 2 years ago
 2 years ago
adunb8 Group Title
linear algebra question I know what R^3 or R^2 or R is but what is F, F^infinite and F1, F2, F3 ?? stuff like that i dont understand
 2 years ago
 2 years ago

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estudier Group TitleBest ResponseYou've already chosen the best response.1
F is usually a field, R^n being an example and other well known being complex or rational numbers .
 2 years ago

adunb8 Group TitleBest ResponseYou've already chosen the best response.0
when you say its a field what does that mean? i gotta see like an example for it.. For example i know that R^2 = (a,b) < dimension of two but i dont know how to do F stuff is there some kind of chart?
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
F is just an arbitrary field. When you say\[\mathbb{R}^2\]you mean\[(a,b), a,b\in \mathbb{R}\]all ordered pairs where a and b are in R. When you say\[\mathbb{F}^2\]we mean\[(a,b),a,b\in\mathbb{F}\]all ordered pairs where a,b come from the same field.
 2 years ago

adunb8 Group TitleBest ResponseYou've already chosen the best response.0
oh i see but my teacher do like some insane stuff like \[F2= sinx, e^x \]
 2 years ago

adunb8 Group TitleBest ResponseYou've already chosen the best response.0
what would \[F^\infty \] would it be?
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
\[\mathbb{F}^\infty \]would be the set of all infinite sequences. You could write it down as:\[(a_1,a_2,a_3,a_4,\ldots\]where\[a_i\in\mathbb{F}\]
 2 years ago

adunb8 Group TitleBest ResponseYou've already chosen the best response.0
oh so \[F\] is just another arbituary field like \[R \]
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
Right. In most of linear algebra, we never use the properties that are specific to R (things like completeness, etc). We only use the field properties of R. So in the theory of linear algebra, we can talk in the most general of settings, an arbitrary field.
 2 years ago

joemath314159 Group TitleBest ResponseYou've already chosen the best response.1
Everything we prove will of course work if we are in R, but it could also work for any field, whether its the complex numbers, or even finite fields.
 2 years ago

adunb8 Group TitleBest ResponseYou've already chosen the best response.0
i get it know but is there like a structure i need to follow? for example \[P2 =[ax^2+bx+c  a,b,c \in R ]\]
 2 years ago

adunb8 Group TitleBest ResponseYou've already chosen the best response.0
and like M2X2 is using the matrices.... is there any particular for \[F\]
 2 years ago
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