- #1
tamintl
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This research project is to help me (I'm an undergraduate) get my head around this topic. It is concerned with affine subsets of a vector space and the mappings between them. As an
application, the construction of certain fractal sets in the plane is considered. It would be considered pretty basic to a seasoned maths student.
I am wanting to learn this so I will be sticking around. I will not just leave. I want to commit to this. Thanks
There are two parts: A and B
If someone is willing to help, I will post each topic AFTER I have fully understood the previous topic. This way it will run in a logical order.
PART A:
----------------------------------------------------------------------------------
Throughout Part A, V will be a real vector space and, for a non-empty subset S of V and
a ε V , the set {x+a: x ε S} will be denoted by S + a
----------------------------------------------------------------------------------
TOPIC 1: Definition of Affine Subset:
An affine subset of V is a non-empty subset M of V with the property that λx+(1-λ)y ε M whenever x,y ε M and λ ε ℝ
To illustrate this concept, show that:
M = { x = (x1,...x4) ε ℝ4 : 2x1-x2+x3 = 1 and x1+4x3-2x4 = 3}
is an affine subset of ℝ4.
I'm not so sure where to start. Opinions welcome
Regards
Tam
application, the construction of certain fractal sets in the plane is considered. It would be considered pretty basic to a seasoned maths student.
I am wanting to learn this so I will be sticking around. I will not just leave. I want to commit to this. Thanks
There are two parts: A and B
If someone is willing to help, I will post each topic AFTER I have fully understood the previous topic. This way it will run in a logical order.
PART A:
----------------------------------------------------------------------------------
Throughout Part A, V will be a real vector space and, for a non-empty subset S of V and
a ε V , the set {x+a: x ε S} will be denoted by S + a
----------------------------------------------------------------------------------
TOPIC 1: Definition of Affine Subset:
An affine subset of V is a non-empty subset M of V with the property that λx+(1-λ)y ε M whenever x,y ε M and λ ε ℝ
To illustrate this concept, show that:
M = { x = (x1,...x4) ε ℝ4 : 2x1-x2+x3 = 1 and x1+4x3-2x4 = 3}
is an affine subset of ℝ4.
I'm not so sure where to start. Opinions welcome
Regards
Tam