Talk:Linear algebra

Dual Map

Is this not backwards?

For every linear form h on W, the composite function f∘h is a linear form on V.

Shouldn't that be h∘f ?

John G Hasler (talk) 01:42, 8 February 2019 (UTC)

 Fixed D.Lazard (talk) 09:11, 8 February 2019 (UTC)

Definition of Linear System

The linear system presented in the "linear system" section of this page seems to contradict the definition of linear systems given by Wikipedia -> https://en.wikipedia.org/wiki/Linear_system. In the definition, a system must have the properties of superposition and homogeneity. The linear system present here does not have either. In particular, this page implies that $y=mx+b$ could be a linear system, while https://en.wikipedia.org/wiki/Linear_system states that it cannot be ($y=mx+b$ has neither the property of superposition nor homogeneity). Note that $y=mx$ is linear with regard to both pages. How can this conflict be resolved? Flexpicker (talk) 19:55, 9 October 2019 (UTC)

The equation $y=mx+b$ is a trivial system of one equation in one unknown. I think we can say that this system has the properties of superposition and homogeneity in a trivial sense. In fact, some systems of several equations which have no unique solution reduce to $y=mx+b$. While considering your post, I looked at the articles Linear algebra, Linear system, and System of linear equations and noticed other problems. They needed a definition and citations. I made some edits to them and hopefully clarified some things.—Anita5192 (talk) 23:01, 9 October 2019 (UTC)

Re: Ottoman textbook

@Anita5192: Re: this edit

I figured the edit explained itself, as it is a public domain textbook by an Ottoman mathametician and diplomat, Hussein Tevfik Pasha, from the 1800s. The textbook's title was "Linear algebra" so the connection to the topic is quite clear.

Secondly of course "Unexplained removal" alone is an acceptable reason to revert, but I feel "unexplained addition" is less so without an explanation on why the addition was not good. WhisperToMe (talk) 05:14, 20 December 2019 (UTC)

Why is it significant to the history of linear algebra? — Anita5192 (talk) 05:35, 20 December 2019 (UTC)

Doing a Google Books search for "Tevfik pasha linear algebra" (some of the pages are not freely available) shows his works being described by books about the development of science in the late Ottoman Empire. The quotes "One of the most important Ottoman scientists in the late 19th century was Hüseyin Tevfik Pasha (1832-1901). [...] of mathematics such as quartanions, the results of which he published in English in a book titled „Linear Algebra" in the year 1882." are from Mitteilungen published by ÖGW, 1997, p. 183. The quote "Among them Linear Algebra written in English by Vidinli Hiiseyin Tevfik Pasha is noteworthy as a valuable contribution to the development of linear algebra. This book, which is concerned with three-dimensional linear algebra and its[...]" is from Science, technology, and industry in the Ottoman world (2000), page 43. He seems to get a lot of coverage from sources based in Turkey, like this one.

Also of consideration is the relative lack of public domain materials. If there are books that are considered to be more influential to the history of linear algebra that are public domain (published in the US before 1923, and/or author died over 70 years ago in most countries), I would really appreciate it if these books are located and uploaded.

WhisperToMe (talk) 06:32, 20 December 2019 (UTC)

I also don't think this book was significant outside of the Ottoman Empire, but I might be wrong about its impact. BernardoSulzbach (talk) 14:04, 22 December 2019 (UTC)

Applications Source Not Cited or Formatted Correctly

I don't know how to correctly add a citation to a particular linear algebra textbook.ScientistBuilder (talk) — Preceding undated comment added 01:46, 31 January 2022 (UTC)

I might be able to help you with this. What is the textbook's name, author, publication date (and edition if there are several)? Anton.bersh (talk) 20:19, 5 February 2022 (UTC)

David C. Lay Linear Algebra and It's Applications 6th Edition. @Anton.bersh ScientistBuilder (talk) 02:02, 18 February 2022 (UTC)

Too Technical for Normal Readers

This article is too technical for people wanting to learn linear algebra. I want to create a new article that does not discuss bijections and mappings and other abstract concepts. I want to create an article that gives concrete examples of matrices, vectors, row reduction, span, determinants, eigenvalues, and vector spaces. ScientistBuilder (talk) 02:04, 18 February 2022 (UTC)

While this article should be understandable to a general audience, Wikipedia articles really aren't intended to be tutorials for people trying to learn how to do things. You might be better off working on Wikiversity's content on Linear algebra, that sort of thing is encouraged there. - MrOllie (talk) 02:19, 18 February 2022 (UTC)