Talk:Linear algebra

Finite fields

In computational number theory you sometimes get people doing linear algebra on matrices made out of integers modulo a prime. Often the prime is 2, but larger ones are also used.

My guess is the elements have to be from a ring or maybe a field. Anyway something with a group operation on the whole set, another group operation on the set except for identity of the first group, distributive law between the two group operations.

Anything to do with finite fields? --Damian Yerrick

Fields and rings

You can do linear algebra over any field. If you're working with rings, they're called modules. Modules share many of the properties of vector spaces, but certain important basic facts are no longer true (the term dimension doesn't make much sense anymore, as bases may not have the same cardinality.) --Seb

Striking (wrong) example

Quoted from the main page:

A vector space, as a purely abstract concept about which we prove theorems, is part of abstract algebra, and well integrated into this field. Some striking examples of this are the group of invertible linear maps or matrices,

This is truly a striking example :-)

Toby Bartels and I are going to correct this and I think we're also going to write about linear algebra over a rig (algebra) (this is not a typo!). -- Miguel

@Miguel @Toby Bartels No rig?

How did Hamilton name vectors?

Quote from the article: "In 1843, William Rowan Hamilton (from whom the term vector stems) discovered the quaternions."

Huh? I didn't find the answer on a quick perusal of the William Rowan Hamilton article either. I didn't see it in quaternions either. It sounds like an interesting story, but what (or where) is the story? Spalding 18:25, Oct 4, 2004 (UTC)

Well, it's there now. —Lowellian (talk)[[]] 23:05, Oct 7, 2004 (UTC)

Equivalent statements for square matrices

This is not an elegant section: it feels slightly like a dumping ground for a bunch of facts. Did anyone else have the same feeling? (Yiliu60)

Yes. Jitse Niesen (talk) 6 July 2005 09:21 (UTC)

Vote for new external link

Here is my site with linear algebra example problems. Someone please put this link in the external links section if you think it's helpful and relevant. Tbsmith

http://www.exampleproblems.com/wiki/index.php/Linear_Algebra

Lists per Axler

Please add some discussion of "lists" as used by Axler in Linear Algebra Done Right. 184.158.0.11 (talk) 12:53, 10 October 2017 (UTC)

Why?—Anita5192 (talk) 17:55, 10 October 2017 (UTC)

Inclusion of link to Essence of Linear Algebra video series

Currently there exists a popular ~2 hour long series of videos on Youtube known as Essence of Linear Algebra which briefly touches upon core topics in linear algebra, providing a visual depiction as well as intuition for why these concepts were created and what they are used for. I believe it is a valuable resource which presents information in a way that a text and image encyclopedia cannot. Upon adding this though it was removed with the person removing it clarifying on their talkpage that it was removed for not meeting the criteria of a reliable source. However, WP:RS specifically states that the reliability of a source is inextricably linked to the statement that it is being used to support. Since external links are not being used to support any statements, this would make consideration of whether or not an external link is a reliable source a moot point. To further support this, WP:EL makes no mention of a link's reliability, only requiring that it be accurate, and WP:ELPEREN (a non-official supplement) explicitly states that reliable sources and external links have different criteria. With this in mind I would like to reintroduce the link into the external links section. Thank you for your time. JustOneMore (talk) 06:53, 26 July 2018 (UTC)

For an alternative point of view consider Wikipedia:NOTYOUTUBE (an essay, not policy). While I prefer to couch my objections in terms of reliability, the real issue is Wikipedia:Verifiability and nothing on Wikipedia is exempted from that. --Bill Cherowitzo (talk) 22:31, 26 July 2018 (UTC)

WP:NOTYOUTUBE is specifically addressing videos embedded into articles, and recommends users to instead link to them via the external links and then redirects them to the external links guideline. WP:Verifiability is explicit in referring to "any of the information within Wikipedia articles". It does not apply to material that is linked to, and it would make no sense to try and apply it that way. Consider a source being used to support claim A. The source is perfectly suited to support claim A, but the source also makes the dubious claim B. By your logic we could not use this source to support claim A because then we would be linking to a source that makes unverifiable claims. JustOneMore (talk) 23:39, 26 July 2018 (UTC)

I have seen the first video of the link. It is a very good explanation of the different points of view on linear algebra (geometric, numerical, abstract), and their relationship. It is unclear whether this can be found in any of the numerous textbooks that are cited, and it is also unclear whether this can be converted in an encyclopedic style. Thus it fits the third condition of WP:ELYES ("Sites that contain neutral and accurate material that is relevant to an encyclopedic understanding of the subject and cannot be integrated into the Wikipedia article due to ..., or other reasons."). Thus I am in favor of keeping the link. However, the explanation sentence must be changed into something like

• Essence of linear algebra, a video presentation of the bases of linear algebra, with emphasis on the relationship between the geometric, the matrix and the abstract points of view

D.Lazard (talk) 10:39, 27 July 2018 (UTC)

I've seen the entirety of the series, and I agree with D.Lazard's assessment. The suggested description is fine, except "bases" should be "basics". XOR'easter (talk) 00:32, 1 August 2018 (UTC)

I may have been a bit hasty, there. I know the channel (and part of this series) and it's very good. My main concern is that there is already quite a number of external links there. If anyone wants to revert me, feel free. Kleuske (talk) 13:18, 2 August 2018 (UTC)

Obscure Turkish Reference

I think the reference to Hüseyin Tevfik Pasha's book should be removed. I looked at the English translation of his book on archive.org and it looks like it is a small textbook on very simple Linear Algebra. It doesn't look like it contains any new research nor does it look like a comprehensive textbook of the state of the art at (or near) the time of publication.

To be frank, it looks like it has only been included due to Turkish nationalism. The only reason why I haven't removed it myself is that I don't want to fight the Turkish nationalists. -- Peter Lund, 2018-08-06 — Preceding unsigned comment added by 80.62.117.202 (talk) 07:38, 06 August 2018 (UTC)

Understandability

I'm trying to learn something about linear algebra because I want to understand eigenvectors so I can read an article I have. The first part of the article was good; but then we get to the sideways "e" which means identical to? Then couldn't the section "Linear Transformations" be simpler? It's important to write for non-mathematicians. Edlong (talk) 22:32, 14 August 2018 (UTC)