User talk:Gbgustafson

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Cheers! prime mover (talk) 08:21, 27 September 2019 (EDT)

6 October 2019

Edited the current proof of the Banach Fixed Point Theorem. Not sure how new theorems are submitted. First attempt was to edit an existing proof. I proceeded by example from other pages. It took about a week to get used to the House Style, which uses macros and environments similar to my own used for books, monographs and papers.

14 October 2019

R.Gow in the Irish Math Bulletin 28 (1992), p 45, uses the term "Vandermonde matrix" as the transpose of the Vandermonde matrix as currently defined in ProofWiki and Wikipedia. I also saw a difference in definitions for interpolation problems, especially Wikipedia.

There are enough variants of the Vandermonde matrix (is "Vandemonde" a spello of Gow's?) that I wonder whether we're due for a refactoring so as to explicitly document them all and explain the nuances. Admittedly the differences are more-or-less trivial (1-based vs x-based, transposes of each) but may be profitable for a newcomer. Thoughts? --prime mover (talk) 10:08, 14 October 2019 (EDT)

Missing "r" in Vandermonde was my typo, a cheap keyboard feature. The nuances are already covered in what exists on the page. I vote NO for explaining nuances.

Alexander C. Atiken (1939) cites (page 50) Vandermonde (1771) as the founder of notation and calculus for determinants, but uses the term "alternant" for what is defined in ProofWiki as a "Vandermonde determinant." Aitken's source for history is Muir's volumes on the history of determinants. I will add a reference to alternants and to Aitken's book. Aitken never used any form of Vandermonde's matrix except the first form on the ProofWiki page, ones in column 1, using term "alternant", e.g., A(0123) in his notation.

15 October 2019

Edits to Vandermonde and Aitken acknowledged and appreciated. All proofread. Edits appear correct.

15 October 2019

Help:FAQ and Help provided less than 5% of the information that I needed to get started. More admin effort is not requested.

The help pages and documentation here are very much underdeveloped, so I think this is fair. Caliburn (talk) 08:26, 16 October 2019 (EDT)

No matter how we dictate the precise structure of the site, and no matter how many links we generate and present to the users to point to them, it will never be enough.

We like to hope that contributors can learn by example: to see what's currently being done and doing likewise. Some manage well at this. Others, who are familiar with other systems, and have their own preferred method of working, have more difficulty. We could spend a lot of time writing many pages of detailed instructions as to how to craft a page on $\mathsf{Pr} \infty \mathsf{fWiki}$, but (at least for me) life's too short. --prime mover (talk) 19:37, 16 October 2019 (EDT)

17 October 2019

 I read the messages from Caliburn and prime mover. All of the reasons supplied were already known to me from reading user talk on the site. I agree that documentation is a moving target and admins have their hands full. Further, it is extremely difficult for site maintainers to guess what a new contibutor will need in terms of what to read first and how to find information. I have some ideas which could be implemented, but I also don't have the time to do it. So I don't expect anyone else is going to rise from the flames to do it either. Thanks for the feedback!

Briefly and cordially: please don't worry too much about the fine details. Accept that your edits will be tweaked in possibly minute ways, possibly major ways, while a {{tidy}} tag sits on your page indefinitely. As time goes on and you contribute more, you may well develop a feel for the structure of a page as a process of familiarization, depending on whatever other outlets you have and whether the house style clashes with your own preferred style. --prime mover (talk) 07:49, 17 October 2019 (EDT)

Created Vandermonde Matrix Identity for Cauchy Matrix from a draft which has 3 examples. Could not find a page that has one theorem and 3 examples, so I can finish. In a mad attempt I created empty pages that were designed like Proof 1, Proof 2, PRoof 3 pages. This failed.

check out Category:Examples, plenty of stuff there --prime mover (talk) 19:21, 17 October 2019 (EDT)

I misunderstood code for included files. Picture the 'Sputnik Monkey'. Thanks!

Vandermonde Matrix Identity for Cauchy Matrix/Example 3x3 <== populated 18.10.2019 and working.

18 October 2019

Failed experiments to be deleted, both pages empty.

Vandermonde Matrix Identity for Cauchy Matrix/Example 1 <== Kindly delete

Vandermonde Matrix Identity for Cauchy Matrix/Example 2 <== Kindly delete

23 October 2019

Sum of Elements in Inverse of Vandermonde Matrix should have an empty proof and

==See also ==

Sum of Elements of Invertible Matrix

Right now it reads like the reference is the proof. It is not.

It may not actually be a proof, but it won't take much effort to turn it into a proof. Such a line does not go into an "Also see" section (for consistency, not "See also") as that is reserved for tangentially-related material of which may be of interest. --prime mover (talk) 15:28, 23 October 2019 (EDT)

Sum of Elements in Inverse of Vandermonde Matrix edited to supply the proof using Sum of Elements of Invertible Matrix.

External email

Usually best not to email contributors directly, but discuss any issues within the website. Otherwise your messages may (with a high possibility) not be answered. Contributors may be reluctant to reveal their direct email addresses.

Your message:

"The example reports one of the two possibilities, the second being z1,z2 in reverse order."

invites the response:

Well all very well, but there's nothing about that on the amendment to the page you submitted.

The formatting had been compromised and the grammar had become inaccurate, and apart from some extra words near the end, there was nothing that said anything different from what was already there.

Maybe I'm missing something, but all I could see was that the page had been changed for no apparent improvement.

--prime mover (talk) 11:26, 30 October 2019 (EDT)

Noted. GBG.

30 October 2019

Ready to post Viète's Formulas with induction proof that uses $e_m\paren { U}$. The extension to rings has not been done. An encyclopedia reference (2001) has a statement for fields. The theorem below is written for real and complex numbers. Undecided are the correctness of the statement and proof which was presented for the ring case.

Vieta's Theorem (draft)

Let

$\map P x = a_n x^n + a_{n - 1} x^{n - 1} + \dotsb + a_1 x + a_0$

be a polynomial of degree $n$ with coefficients real or complex numbers.

Let $z_1, \ldots, z_k$ be real or complex roots of $P$, not assumed distinct.

Suppose $a_n$ is nonzero and:

$\ds \map P x = a_n \prod_{k \mathop = 1}^n \paren {x - z_k}$

Then:

\(\ds \paren {-1}^{k} \dfrac{ a_{n - k} } { a_n }\)

\(=\)

\(\ds \sum_{1 \mathop \le i_1 \mathop < \dotsb \mathop < i_k \mathop \le n} z_{i_1} \dotsm z_{i_k}\)

for $k = 1, 2, \ldots, n$.

Equivalently:

\(\ds \paren {-1}^{k} \frac { a_{n-k} } { a_n }\)

\(=\)

\(\ds e_{k} \paren { \set {z_1,\ldots,z_n} }\)

Elementary symmetric functions

Listed explicitly:

\(\ds \paren {-1}\, \dfrac { a_{n-1} } { a_n }\)

\(=\)

\(\ds z_1 + z_2 + \cdots + z_n\)

\(\ds \paren {-1}^2 \dfrac { a_{n - 2} } { a_n }\)

\(=\)

\(\ds \paren {z_1 z_2 + \cdots + z_1 z_n} + \paren {z_2 z_3 + \cdots + z_2 z_n} + \cdots + \paren {z_{n - 1} z_n}\)

\(\ds \)

\(\vdots\)

\(\ds \)

\(\ds \paren {-1}^n \dfrac { a_0 } { a_n }\)

\(=\)

\(\ds z_1 z_2 \cdots z_n\)

2 Nov 2019

Example added: Recursion Property of Elementary Symmetric Function which is to be used in the proof of Viete'a formulas. The example illustrates for elementary symmetric functions a divide and conquer method to deal with subscript and summation Hell.--Gbgustafson (talk) 07:35, 2 November 2019 (EDT)

Example

Let $\set {z_1, z_2, \ldots, z_{n+1}}$ be a set of $n+1$ values, duplicate values permitted.

Then for $2 \le m \le n$:

$e_m \paren { \set {z_1,\ldots,z_n,z_{n+1} } } = e_{m-1} \paren { \set {z_1,\ldots,z_n} } + z_{n+1} \, e_m \paren { \set {z_1,\ldots,z_n} }$

20 Dec 2019

I read the history for Karl Frei in 2018. --Gbgustafson (talk) 06:03, 20 December 2019 (EST)

Good. KarlFrei (talk) 13:03, 22 December 2019 (EST)