- #1

musicgold

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- 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