Dual Space Q: What does the dual space of R^2 consist of?

[joeyjoejoe]

I am teaching myself some advanced linear algebra.

As a simple question, what does the dual space for R[sup:3aqq1qur]2[/sup:3aqq1qur] consist of? The only linear functionals that I can think of are the standard ones, assigning vector coordinates to a vector length and to the angle to the positive x-axis. But there would seem to be more variations of these functionals (dilations, rotations, etc....)

I can't seem to wrap my head around what I'm reading.

What does the dimension of R[sup:3aqq1qur]2[/sup:3aqq1qur] imply about the "size" of it's dual space?

 

[pka]

I am teaching myself some advanced linear algebra. DANGEROUS
As a simple question, what does the dual space for R[sup:jzpc4jso]2[/sup:jzpc4jso] consist of? The only linear functionals

You must understand that word LINEAR.
Any linear functional on \(\displaystyle \Re^2\) has the form \(\displaystyle ax+by\).