Wikibooks:Featured books/Nominations/Addition/Linear Algebra

Linear Algebra
I would like to nominate Linear Algebra as a featured book. I think it is by far the most complete, well written mathematics text we have. It contains diagrams where it should, navigation templates, index, TOC, etc. It does currently contain cleanup tags, but not in the text, but rather in the "old pages." (So it violates criteria 8.) But these pages are no longer really part of the book (so maybe it violates 9 too?). But overall, I think these minor issues should be over looked. Thenub314 (talk) 15:09, 1 May 2010 (UTC)


 * Comment User: JimDavies. I'm trying to learn linear algebra from this book right now, and I've only gotten started, but I already have problems with it that I'd like to express. It starts out, in the chapter on Gauss' Method, with a definition of linear equations that is highly mathematical, and is not accompanied by an easy-to-understand English version to scaffold learning. Something like "Basically, it's a bunch of numbers times variables added together to equal a number" would help a lot, and help the mathematical definition make sense. Is this a reference book for linear algebra, or a book to learn it? I'm assuming it should be a book for learning it, but it's not written like that. On the same page, we get even as far as example 1.8 and there's still no explanation of why the examples do what they do or why. For example, the goal of the echelon form is, I think, to get the final equation in a form so that one of the variables becomes easy to calculate with algebra. But it doesn't say this anywhere. —Preceding unsigned comment added by Wbjimmyd (discuss • contribs)
 * [[Image:Symbol comment vote.svg|15px]] Comment Hi JimDavies, your correct that this is a book to learn from and not a mathematical reference book.  In fact, the book is used as a textbook for a course given at Saint Michael's College.  But your correct the book is not perfect.  An attempt to give the plain english explanation of a linear equation is given at the section before, but it focuses more on the power of the variables and not the numbers in front.  And the explanation of Echelon form, for some reason, comes at the end of the section.  I think it could be very helpful if you left complaints in the books discussion pages as you go along.  Also see 33rogers's comments below, he is correct that Wikipedia does a lot to give plain english explanations, and very good resource for readers.  Also don't miss out, on the other Resources given there, like the video lectures given by Gil Strang.Thenub314 (talk)
 * Symbol support vote.svg Support Verifying the accuracy of the content is beyond the scope of my personal knowledge, but I will say that it looks nicely presented and I trust Thenub314's ability to deal effectively with mathematics. -- Adrignola talk contribs 16:17, 1 May 2010 (UTC)
 * Support - I don't have the faintest idea what the books is about - you know, that is why I edit the geometry for elementary school book, I'm only a grade above that - but it sure looks nice.  Kayau  David Copperfield  MOBY DICK   the great gatsby  00:59, 2 May 2010 (UTC)


 * [[Image:Symbol comment vote.svg|15px]] Comment Many Mathematics books can be confusing at times, therefore I suggest linking to the appropriate Wikipedia article as I have done on this chapter *Reduced Echelon Form. I believe linking to Wikipedia will make it more easier to understand the book, as some may give up if they do not understand some chapters.
 * I have already tagged the Gauss' Method, Reduced Echelon Form, Gauss-Jordan Reduction, Matrix Multiplication, and Mechanics of Matrix Multiplication with the corresponding Wikipedia articles. revisions undone --33rogers (talk) 09:03, 6 May 2010 (UTC)
 * Further to that concerns here Talk:Linear_Algebra have not been resolved. --33rogers (talk) 11:22, 6 May 2010 (UTC)
 * [[Image:Symbol comment vote.svg|15px]] Comment It is a good idea to provide links to the appropriate wikipedia articles.  As it breaks up the narrative of the book I have moved the links th the Resources section.  Also I have included reciprocal links to this book on those wikipedia pages  (at the end of the article as per wikipedia policy.)  I am confused about which points raised in the order of presentation are still present.  A's concerns about order of presentation were aimed at the old book and not the book donated by Heffron, as [User:Shahab|Shahab]] points out.  The book now follows Heffron's order.  Taku says the book should start with investigating sytems of linear equations, which is what Heffron, and now this book does.  He makes some other general comments about how all of our algebra books fit toegether, but that doesn't seem to be about the book itself.  Taku goes on to suggest it would be nice if we had a much more advanced book, and I agree.  But I think the idea would be to have a second book, because modules, rings, symplectic geometry, etc all usually go well beyond the scope of a first course in linear algebra.  Which issues are still outstanding? Thenub314 (talk) 12:05, 6 May 2010 (UTC)
 * [[Image:Symbol comment vote.svg|15px]] Comment 33rogers, I am curious about your comments above.  Would you like to see every page link to the appropriate wikipedia article? Somehow we tend to link to wikipedia very sparely.   I was following the advice here when I moved the links to a separate section.  Basically I am curious what I can do to win you support (jees I sound like a politician).  Or maybe less politically what do you think it would take to make this a better book? Thenub314 (talk) 12:34, 6 May 2010 (UTC)
 * I just downloaded the copy of the book from ftp://joshua.smcvt.edu/pub/hefferon/book/book.pdf. The name of the book is Linear Algebra; What if it was changed to Jim Hefferon's Linear Algebra? This would remove the concern brought up on the talk page regarding presentation order. And it wouldn't imply as being the authoritative book (per Wikibooks) for learning Linear Algebra. This book seems to be very advanced in nature; that's why, I suggested linking to the corresponding Wikipedia Articles, as they are much easier to read even for beginners (especially when going through the book). --33rogers (talk) 13:13, 6 May 2010 (UTC)
 * [[Image:Symbol comment vote.svg|15px]] Comment  I am a bit uneasy moving Jim Hefferon's name into the title for a few reasons. First the books are diverging.  Prof Hefferon is still developing his text and so are the occasional contributors here.  After 5 years of being on a wiki the two books might not look at all alike.  To the best of my knowledge no other books here include an author's name here at wikibooks.  Though I don't think it is explicitly against any the naming conventions, it would be a bit strange.  Finally, it strikes me as against the spirit of the copyright he released it under. By the CC-SA license we must not attribute the author in any way that suggests he endorses the derived work.  Having his name as part of the title might be misconstrued as his endorsement.  But I am happy to consider other titles.  I actually had thought of renaming it myself, but couldn't think of any other titles that seemed appropriate.
 * But moving the pages so they have a new name will not quite solve the problems. Perhaps it makes more sense to archive the talk page?  I will go through now and add some more wikipedia links. Thenub314 (talk) 14:58, 6 May 2010 (UTC)
 * Even better would be to link to other book pages here, if possible, that explain any beginning concepts. Also, prerequisite can be used on the main page to indicate another book that should be read before this one, alleviating the concern that the book doesn't cater to the proper audience. -- Adrignola talk contribs 15:19, 6 May 2010 (UTC)

A good idea. The introduction mentions the book requires calculus. Since the Calculus book here needs a lot of work I wanted to weaken the wording of the standard prerequisite box a bit to make sure it was clear knowing calculus from any source was sufficient, but we do have a book on calculus if you don't already know it. Thenub314 (talk) 15:54, 6 May 2010 (UTC)


 * I changed Oppose to Comment. --33rogers (talk) 16:49, 6 May 2010 (UTC)
 * For the record, I wish to recommend the Book Finite Mathematics for Business, Economics, Life Sciences and Social Sciences by Raymond A. Barnett, Michael R. Ziegler, and Karl E. Byleen. (no pre-requisites i.e. studying Calculus) --33rogers (talk) 17:01, 6 May 2010 (UTC)

Support Many of the issues about content presented here stem from the fact this book is (as the Introduction implies) targeted at Mathematics undergraduates, and not at students of other fields that have introductory Linear Algebra courses (I know for a fact students would go crazy if this book was used for a first-semester course on a Chemistry program). That fact explains, for instance, why the book demands Calculus as a pre-requisite, or why it only starts discussing matrices and determinants after seemingly advanced conceptual discussions. While it would be very useful to have an introductory, more practical book on Linear Algebra for students of natural sciences (and maybe to state the target audience of this book more explicit as well), the fact remains that the book is (as far as I could tell by quickly skimming it) of very good quality, and deserves featured status. --Duplode (talk) 17:28, 14 May 2010 (UTC)


 * Thenub314: Would you consider renaming the book to Linear Algebra for Math Undergrads?
 * This will remove my concern regarding Criteria #2: Have a suitable definition (target audience, scope and style).
 * PS. If it is moved to the above title, (or Linear Algebra for Mathematics undergraduates or similar), I will gladly support the nomination.
 * --33rogers (talk) 17:35, 18 May 2010 (UTC)


 * Since you ask me directly, I would have to say I am not found of specifying the audience in the title. It is rather a double edged sword, it might scare away people who could benefit from the book.  At the same time to stronger students it may seem a bit too watered down to be seriously called an introduction for mathematics majors.  So depending on the university, it may be seen as too easy or too hard.  This makes me pause before giving labeling it "for Mathematics Undergraduates", I have a feeling that would make very few people happy.
 * The book was designed specifically for students who had not previously been exposed mathematics as mathematicians view it (that is, as a subject whose main goal is to prove theorems). And attempts to build students up from a background that lacks mathematical theory.  At the same time it views itself as a pure mathematics text, and so it passes up on obvious applied topics such as LU decompositions which follow easily enough from the material covered.  Coming up with a title that correctly gives the flavor of the book is difficult.  I suppose I think something like Linear Algebra: An Introduction to Mathematical Discourse.
 * At the end of the day I am just the translator, so I am not too picky about the title. If you strongly feel it should be Linear Algebra for Mathematics undergraduates then I only ask you capitalize undergraduates, and go ahead and put a request for it to be moved by an admin. (Since they can move multiple pages at once.) Normally I would wait for your reply here and do it myself, but real life might be keeping me busy in the near and foreseeable future.
 * As for Criteria #2, the question really is how do we expect the book to define its target audience and scope? Most of this book's introduction is a discussion exactly trying to define these two ideas. Overall I feel it meets Criteria #2, but I see how this could be missed if the introduction is not read. Maybe the feeling is that the book doesn't do enough to advertise this?  Thenub314 (talk) 22:04, 18 May 2010 (UTC)
 * I wouldn't be very keen on adding "for Math Undergrads" to the title either. Maybe a tiny (just a couple sentences) foreword in the front page of the book telling readers of the general approach Thenub has just spoken of could be enough. --Duplode (talk) 02:22, 19 May 2010 (UTC)

Thenub314: I just felt that the title Linear Algebra is too generic title for a book like this. And due to the title, I felt it failed Criteria #2 & #4. I suggested a solution for Criteria #4, which was to link the chapters to the corresponding Wikipedia Articles, to complement the book, for example using the template. However, since you found that not to be appropriate, and undid all my revisions to the book, I suggested that Title of the book be changed. Considering there is opposition to the title Linear Algebra for Mathematics Undergraduates, I say go ahead and move it to your title Linear Algebra: An Introduction to Mathematical Discourse. --33rogers (talk) 05:46, 19 May 2010 (UTC)

Support But I would like those links to Wikipedia to be in the modules, instead of being only at Linear Algebra/Resources, and maybe the book could be renamed to something like "An Introduction to Linear Algebra". Helder 23:53, 21 May 2010 (UTC)
 * I don't think the book should be renamed Introduction to Linear Algebra, as there is no Intermediate Linear Algebra or Advanced Linear Algebra as far as I know. Kayau ( talk &#124; email &#124; contribs ) 01:14, 22 May 2010 (UTC)
 * Well, there is "Advanced Linear Algebra", from Springer... So "Introduction to Linear Algebra" could be a good name. Helder 15:44, 24 May 2010 (UTC)


 * In the end I suppose Helder is right about the placement of the links to wikipedia. Only if having a list of 30 wikipedia links at the end doesn't seem very helpful.  On the other hand having the links in a box in the beginning of the article is quite distracting, and disrupts the flow of the book.  My suggestion would be to include wikipedia links I think is best done at the end of the article just after the references or exercises as appropriate.


 * While attempting to add links I came across various difficulties. These are the difficulties I forsee adding wikipedia links. There is not always a 1-1 correspondence of modules here and wikipedia pages. Where wikipedia might have one module we might have one chapter, where we have several sections in a module wikipedia might have individual  articles.  The second case is easy to handle.  The first case is a bit annoying because there is no natural place to put the wikipedia link.


 * Another problems are about differences in content. Let me give some examples.  First, this book proceeds axiomatically with regards to the determinant and leaves the existance to an optional section.  This order of approach is rather unique, designed to keep from overwhelming the students with complicated formulas right away as well as  moving tedious and uninformative proofs out of the main discussion.  While I am not particularly endorsing or condemning this approach, it seems counter productive to link to the wikipedia article in too early a module, because that article which will gets to the formulas more or less right away.  Thereby ruining the work of trying to delay them.  A similar problem is that this book attempts to restrict to real vector spaces whenever possible, while the wikipedia articles attempt to be as general as possible after the first few paragraphs.


 * Also, the articles on wikipedia also get quite technical, or at least pseudo-technical, with more mathematical topics. The articles there now about more matrix related topics are ok, but once we get into linear maps and vector spaces I forsee a problem.  Let me explain that by technical I mean that the wikipedia articles occasionally go on to explain how things work in more settings such as Banach spaces, vector spaces over other fields and other topics well beyond this book.  By pseudo-technical I mean they favor technical wikilinked terms like Endomorphism which the readers of this book will not be introduced to and following wikilinks around quickly gets you to abstract territory.  I remain not so picky about the title, there is a lot of merit in Helder's suggestion. The only potential difficulty is that some may mistake it to be a synonym for  "Introductory Linear Algebra".  Books starting with "Introductory" are generally much easier then books starting with "Introduction to", so maybe some will think it is too difficult for this title.  Thenub314 (talk) 10:17, 25 May 2010 (UTC)
 * And what about "A First Course in Linear Algebra"? Would it be less confusing for the readers?
 * About the links to other projects (particularly to Wikipedia), in some places it is possible to have the links in a sentence like (after e.g. a definition which was given only for vector spaces over R) "in some contexts it is desirable to work with this concept over fields other than R. The interested reader is suggested to read the Wikipedia article on ... ". The same applies when we are "moving tedious and uninformative proofs out of the main discussion": a simple phrase could suggest the reader to look either at the appendix or the Wikipedia article... Helder 16:45, 27 May 2010 (UTC)
 * The title should not make it seem that it is very easy for a person who has no knowledge of calculus, to think this is where they would learn about Matrices etc. There are other books as mentioned earlier that can get the job done (teach you Linear Algebra) without the pre-requisite of knowing atleast 1st Year (2 courses of) Calculus. --33rogers (talk) 09:11, 28 May 2010 (UTC)

Unrelated note: The word 'module' is not used on Wikipedia. The word 'article' is used instead. 'Pages' will also do, though it doesn't just refer to the mainspace. Kayau ( talk &#124; email &#124; contribs ) 02:28, 29 May 2010 (UTC)

I have often argued we should call "modules" pages instead, maybe we should make a formal proposal in the reading room


 * This conversation has been stalled for a while now maybe it is time for someone to call it one way or the other. Thenub314 (talk) 17:02, 1 July 2010 (UTC)


 * Go ahead. It's the summer of proposals.  As for this book, I say feature it.  You've got nothing but support above and the neutral comments are from those who  fully understand the book's scope. – Adrignola talk 17:10, 1 July 2010 (UTC)


 * OK. I hesitated closing the conversation since I was the one who started it. I always thought guideline 1 at WB:DP was good advise I try to follow most of the time.  When you feel strongly about something it is easy to miss interpret what other people have written. But your right, there are no real opposing positions above, so I shouldn't worry about it. Thenub314 (talk) 18:55, 1 July 2010 (UTC)

I would be inclined to say either no consensus or not done. Two people that are in support of featuring this book admit they don't know what the book is about or if its accurate. A third supporter appears to be unhappy with the absence of Wikipedia links or the title of the book. A reader of the book apparently thinks there are parts that could be better written. --dark lama  19:27, 1 July 2010 (UTC)


 * Maybe I will recuse myself from the final decision. I have spent too many hours staring at an emacs window to be unbiased. Thenub314 (talk) 21:07, 1 July 2010 (UTC)

As the person who closed this discussion (a few hours ago, as "not done &mdash; lacking clear consensus"), I'd like to reopen it, and ask a question. My question is: Where should this book go from here? I'll elaborate. In deciding how to close the discussion, I consulted precedents in the archive for what does and doesn't suffice as consensus to promote to featured-book status, and it seemed to me that successful votes were more clear-cut than this one has been. That left the question of whether to leave the discussion open, which I based (naively, at best) on the fact that I didn't see how subsequent developments in this discussion could turn it into something clear-cut enough to qualify as successful. My threshold for certainty on that should probably have been higher, but a much more fundamental mistake was, I think, that the yes/no determination should not be thought of as the whole &mdash;or even necessarily the main&mdash; purpose of the discussion. If the vote isn't successful, it has to be clear how the book can continue to be usefully developed in a way that offers the prospect of future promotion. Closing debate now, with no clear path forward, would be essentially discouraging further development of the book, exactly the opposite of the encouragement that I understand to be one of the major community functions of featured-book status. Until we either promote or say what to do next, I'd be happy to see the discussion stay open indefinitely. --Pi zero (talk) 09:11, 2 July 2010 (UTC)


 * I think what happens next is discussion continues in the book's discussion pages by book contributors and those with issues with the book. Things to consider discussing more in the book's discussion pages might be:
 * Does the book need a new name?
 * Does the scope and audience of the book need to be better defined?
 * Do parts need to be rewritten to be easier to follow and understand?
 * Can missing material be added to reduce or eliminate a need to depend on Wikipedia links?
 * How can this book be made better?
 * --dark lama  10:52, 2 July 2010 (UTC)


 * (Edit conflict. This doesn't take into account the last comment made by DL as I haven't had a chance to read it yet.) Well I will summarize as best I can, but to me like it might be a hopeless case of "you can't please everyone". But maybe someone else can then use this summary to find ways to improve the book and nominate it again when it is ready.  I will bold sentences that I think are the relevant steps forward.
 * One issue is the existence and use of Wikipedia links. One suggestion was to add a link at the beginning of every section to the corresponding wikipedia article (such as, , and ).  My initial reaction was to move these links to the page on external resources section based on the first bullet here.  One solution that could satisfy the objections would be to go through each page and add links to wikipedia through a section at the end of each module.  Unfortunately I don't think this type of linking would be an improvement, due to different definitions, styles, scope, etc that are wikipedia. It is useful to link terms that are not defined in the text as in here and here, to steal some pages from currently featured books.
 * The second issue is the title. This is much tricker.  Some people would like the title to indicate the book is advanced (such as Linear Algebra for Math Undergrads) and some would like to indicate that it is more elementary "A First Course in Linear Algebra".  The difficulty is that there are so many different levels that linear algebra is taught at it is hard to get across this is a "mathematical introduction for those who have not seen many other rigorous courses, and so proves things but avoids unnecessary generality".  But apparently the feeling is that this needs to be made clear in the title, as this is already explained in the introduction and (as a result of the discussion here) at the beginning of the TOC.  A really clever idea for the title is necessary to describe the scope of the book.  I unfortunately have no clever ideas about this. I would like to comment that I think it is a not a good requirement that books should describe their scope via the title.
 * User Wbjimmyd points out that this this book doesn't always give plain english descriptions of some of the objects discussed, and so as DL comments there are parts that could be better written. It is not entirely clear to me if he read the section before or not, as he mention the book begins with Gauss' method but there is actually a section before that attempts do describe what he was complaining about.  I have two ideas to address his concerns, The wikipedia links may address these concerns.  Finally, I don't think people will be truly  happy with this book, its title etc until Two additional books are created, one more basic and one more advanced.  There are lots of unused pages left over from when the two books were merged that haven't deleted yet because I thought they could aid in this task. Thenub314 (talk) 11:28, 2 July 2010 (UTC)
 * DL has a point, though being the unique person who has seriously edited book in the past year this answer this response is equally disheartening. But hopefully "the books contributors" will someday refer to a set with more than one person so some progress can be made. Thenub314 (talk)


 * Maybe the book merge is why people think these things need addressed? Maybe it still seems like two separate books? Maybe you could motivated and encourage the people that criticized the book to help improve it? I guess the book could use some fresh eyes on it. --dark lama  13:20, 2 July 2010 (UTC)


 * I didn't like the sound of the Wikipedia-links idea; Wikipedia links I find generally are a symptom of, rather than cure for, an underdeveloped book. If we can't be definite about what needs improvement, and yet we can't collectively reach consensus to promote, the problem may be with the discussion.  More participants who both understand Wikibooks and consider themselves reasonably qualified in the technical content would help; I might satisfy both criteria, with some elbow grease (because it's been a few years) &mdash; if I could spare sufficient elbow grease, which probably won't happen for at least a couple of months. --Pi zero (talk) 14:33, 2 July 2010 (UTC)


 * I agree the need for Wikipedia links sounds like a symptom of, rather than a cure for, an undeveloped book. I think some people that participated in the discussion were unfamiliar with Wikibooks, but even with that being the case what they said showed there are issues that need addressing and that shouldn't be ignored lightly. That is why I tried to word what I believe people saw as problems with the book in a form that makes since for Wikibooks, in my response to your reopening this discussion above. --dark lama  14:50, 2 July 2010 (UTC)

Linear Algebra
It's a very well-written book on linear algebra, with problems and solutions every chapter. It's a rare gem among technical books here: The presentation is clear, the flow is natural (from what I've read so far), and not at the cost of mathematical precision either. I wholeheartedly nominate this book to be featured. Kayau (talk · contribs) 15:44, 11 July 2016 (UTC)
 * --Jusjih (discuss • contribs) 00:46, 20 December 2017 (UTC)
 * as well. I'm doing some lite editing myself. —Justin ( koavf ) ❤T☮C☺M☯ 05:09, 20 December 2017 (UTC)
 * The LaTeX is not displayed properly into Linear_Algebra/Print_version/Part_1. JackPotte (discuss • contribs) 16:39, 20 December 2017 (UTC)
 * Encik Tekateki (discuss • contribs) 21:14, 9 July 2019 (UTC)
 * Nice book --ЗAНИA [[Image:Flag_of_the_Isle_of_Mann.svg|15px]]talk 08:58, 28 December 2019 (UTC)