- #1

nomadreid

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- TL;DR Summary
- In the brief article cited in the description, the author gives a very limited example of how to interpret the derivative as a matrix. It is unclear how to extend this example to more general cases.

In https://www.math.drexel.edu/~tolya/derivative, the author selects a domain P_2 = the set of all coefficients (a,b,c) (I'm writing horizontally instead off vertically) of second degree polynomials ax^2+bx+c, then defines the operator as matrix

to correspond to the d/dx linear transformation. (We are not dealing with partial derivatives, etc.)

The author then continues with the domain of P_n = the set of all coefficients of n-degree polynomials, and the corresponding (n+1)x(n+1) matrix is defined analogously.

So, the author has defined matrices that correspond to the simple derivative for polynomials in one variable. However, I don't see how you could extend this to functions (of one variable) expressed with non-positive integer exponents. Can one, or does one have to take another tack? If the latter, which?

Motivation for my question: it is said that every linear transformation corresponds to a matrix; since d/dx is a linear transformation, there must be a matrix for it, but .... which?

Thanks in advance.

to correspond to the d/dx linear transformation. (We are not dealing with partial derivatives, etc.)

The author then continues with the domain of P_n = the set of all coefficients of n-degree polynomials, and the corresponding (n+1)x(n+1) matrix is defined analogously.

So, the author has defined matrices that correspond to the simple derivative for polynomials in one variable. However, I don't see how you could extend this to functions (of one variable) expressed with non-positive integer exponents. Can one, or does one have to take another tack? If the latter, which?

Motivation for my question: it is said that every linear transformation corresponds to a matrix; since d/dx is a linear transformation, there must be a matrix for it, but .... which?

Thanks in advance.