Coordinates or Vectors
carlintou
How do we know when the variables/numbers within parentheses are coordinates or vectors? For example, Basis beta = {(1,1), (1,-1)} - is (1,1) a vector or set of coordinates?
richardsun: May 6, 2015, 12:04 a.m.
It's best to think of everything as vectors. That way, it's easier to see the relationship in other types of vector spaces such as polynomials, you can apply the same strategy to all problems
yulduzkhonbruin: May 6, 2015, 12:14 a.m.
When they say "change of basis" they mean change of coordinate, or, change of coordinate vectors. So, it is coordinate vectors. They are always vectors. For example, your basis beta is in R2 with set of vectors (1,1) and (1,-1) in x and y axis with coordinates given by scalars. If you wanna see it in the graph to better understand, they are given in chapter 3.4. I think example 2 is pretty good.
drewgomberg: May 6, 2015, 12:59 a.m.
I believe the best answer to the question is too look for the context of what the numbers and variables are described as. If they describe an stationary object in space they're likely points while if they describe a basis for a vector space they're certainly vectors. I think the differentiation will be clear on the exam contextually.
drewgomberg: May 6, 2015, 12:59 a.m.
I believe the best answer to the question is too look for the context of what the numbers and variables are described as. If they describe an stationary object in space they're likely points while if they describe a basis for a vector space they're certainly vectors. I think the differentiation will be clear on the exam contextually.