 #1
musicgold
 288
 13
 Homework Statement:

This is not a homework problem.
I am trying to understand the difference between polynomials as vectors vs. functions as vectors.
 Relevant Equations:
 I have two sources that show that they are treated differently when represented using vectors.
As per source # 1 ( link below), when treating polynomials as vectors, we use their coefficients as vector elements, similar to what we do when we create matrices to represent simultaneous equations.
However, what I noticed in Source #2 was that, when functions are represented as vectors, the vectors elements are the output values of the function.
1. Why are polynomials and functions represented differnetly?
2. Can a polynomial be represented by a vector the same way as a function is represented?
3. How can a vector model a function that has an infinite range?
Source #1
Source #2
Thanks
However, what I noticed in Source #2 was that, when functions are represented as vectors, the vectors elements are the output values of the function.
1. Why are polynomials and functions represented differnetly?
2. Can a polynomial be represented by a vector the same way as a function is represented?
3. How can a vector model a function that has an infinite range?
Source #1
Source #2
Thanks