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The best linear algebra books

108 点作者 begriffs将近 9 年前

12 条评论

doppioandante将近 9 年前
There&#x27;s a introductory book that I would add to the &quot;generalist&quot; list, that is &#x27;Linear Algebra Done Wrong&#x27; by Sergei Treil. It can be found freely here: <a href="https:&#x2F;&#x2F;www.math.brown.edu&#x2F;~treil&#x2F;papers&#x2F;LADW&#x2F;LADW.html" rel="nofollow">https:&#x2F;&#x2F;www.math.brown.edu&#x2F;~treil&#x2F;papers&#x2F;LADW&#x2F;LADW.html</a><p>I&#x27;ve used it to prepare my linear algebra exam in an italian university (which usually emphasize theory over practice, even in engineering courses), and I&#x27;ve loved it. There are few exercises but they&#x27;re to the point. Complex inner product, self-adjoint operators etc. are treated. I find the notation used in there particularly easy to understand, and proofs are elegant but very easy to follow.
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dxbydt将近 9 年前
Given the frequency and popularity of these &quot;math texts for programmer audience&quot; threads on HN, I think there&#x27;s a solid business model where programmers pay a onetime subscription fee for unlimited email&#x2F;hangouts access to a math professor. The problem with learning math all by yourself is, to quote my favorite math professor- &quot;math is a foreign language&quot;. So its a bit like trying to learn chinese sitting in a non-chinese setting, with only a chinese grammar text. You are simply not going to get very far. Far easier to buy a plane ticket to China and surround yourself with Chinese speakers, so you learn through osmosis - which is what the university experience is all about. But not everyone can take time off and go to a university. So then, atleast have a Chinese mentor on call, who can guide you through the difficult parts, tell you why things are the way they are etc.<p>I&#x27;d be glad to pay $1000 for a 1year unlimited email access to a math prof who can help me with some of the harder portions of measure theory and Banach spaces. Sign up enough students like myself and you have a lucrative gig.
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jacobolus将近 9 年前
So has the author read all these books? Is there a review? What makes these the best? Isn’t a significant part of the content in these books overlapping?<p>What is someone who isn’t a graduate student algebraist supposed to take away from a list of 33 books? At typical textbook prices, that’s like $4000 and 5 years of doing nothing but reading about linear algebra.<p>(Sorry if this sounds negative; I’m sure there’s some audience who will find this list useful.)
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scottlocklin将近 9 年前
I can&#x27;t believe he didn&#x27;t mention Gilbert Strang. This should be the starting point for everyone, IMO.<p>The oddball Russian books look very interesting, but for a computer guy to learn, I&#x27;d suggest Strang, then Trefethen &amp; Bau (my favorite). If there is anything else worth knowing about numeric linear algebra it is in Gollub, or Demmel&#x27;s applied numerical linear algebra (another unforgivable omission; he only helped write LAPACK!).<p>The problem books can also be important; they&#x27;re all pretty good if you pick the problems right.<p>Not sure the highly theoretical stuff is actually worth anything as far as getting things done, unless you go on to study Algebra and mathematics in general. Ultimately the &quot;real world&quot; stuff where linear algebra is studied as systems of equations and geometric constructs is going to be closest to what you actually do with linear algebra on a computer.
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jm547ster将近 9 年前
Really appreciate this effort. My mathematical background is somewhat lacking and I&#x27;d love to pursue ML&#x2F;Data science where I&#x27;m led to believe this is a prerequisite. Anyone able to tell me what other areas of math I might need as a baseline before diving in here?
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swordswinger12将近 9 年前
Why no Halmos, &quot;Finite-dimensional vector spaces&quot;? It&#x27;s pretty theoretical but very approachable also.
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ivan_ah将近 9 年前
The books in the list are pretty advanced. It would be nice to see some sort of &quot;star&quot; rating for each book to indicate which books the authors found best.<p>On a shorter note, here is a four-page introduction to the basics of linear algebra: <a href="https:&#x2F;&#x2F;minireference.com&#x2F;static&#x2F;tutorials&#x2F;linear_algebra_in_4_pages.pdf" rel="nofollow">https:&#x2F;&#x2F;minireference.com&#x2F;static&#x2F;tutorials&#x2F;linear_algebra_in...</a>
liamconnell将近 9 年前
I studied under the author of this book [1] and I can anecdotally say that I finished with a very strong understanding of the subject. Learning linear algebra and being able to whip out some of the less common theorems has been very valuable to me as someone who uses numpy, pandas and tensorflow regularly.<p>[1]: <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Applications-Otto-Bretscher&#x2F;dp&#x2F;0136009263" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Applications-Otto-Bret...</a>
verylongaccount将近 9 年前
I am a big fan of Hoffman and Kunze. I also think many would benefit from reading a book on ordinary differential equations after they read a linear algebra textbook. Much of the elementary theory of linear ODEs consists of combining relatively simple observations with linear algebra. Coddington and Levinson is the one I used for a course in college, but it is quite detailed. I am sure there are less ponderous options available, but I don&#x27;t know any off the top of my head.
SFJulie将近 9 年前
The Lipschutz (that is quoted) is good. While looking stupid and repetitive it is giving very good basis.<p>Applying linear algebrae to grok more complex problems can be done with the Mc Grawhill book on Mechanic (solid &amp; punctual). It is the same pattern : simple explanation and a lot of exercises.<p>Thermodynanmic, quantum mechanics, relativity and electromagnetism are introduction to even more interesting algebrae.<p>Maybe Feynman physics lessons are the right books :)
mathaftermath将近 9 年前
My favorite LA books are Linear Algebra by Friedberg&#x2F;Insel[0] which is a combination of Axler style book with more computation oriented one (Terry Tao has a set of lectures based off this book). Another one I like is Modern Intro To LA by Henry Ricardo[1] which implicitly introduced me to Replacement theorem which is really overlooked in a ton of LA books. Again, this book&#x27;s a rigorous mixture of both theory and computation done very well. If you&#x27;ve never seen higher level math before, there&#x27;s Linear Algebra: Gateway to Mathematics by Robert Messer[2]. It has tons of commentary about elementary set theory and proof techniques along the way. Whenever someone mentions Axler&#x27;s book, someone else brings up Treil&#x27;s book. But there&#x27;s a third one in the same league&#x2F;group which is Linear Algebra: An Introduction to Abstract Mathematics by Robert Valenza[3]. Other favorites are Coding the Matrix by Philip Klein[4] for Python aficionados and Linear Algebra Through Geometry by Banchoff&#x2F;Wermer[5] for those who like geometry.<p>If you are way beyond all this, you can still pick up new things from Advanced Linear Algebra by Steven Roman[6].<p>[0] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Stephen-H-Friedberg-ebook&#x2F;dp&#x2F;B003YNXP7U&#x2F;ref=sr_1_30?ie=UTF8&amp;qid=1469389674&amp;sr=8-30&amp;keywords=linear+algebra" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Stephen-H-Friedberg-eb...</a><p>[1] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Modern-Introduction-Linear-Algebra&#x2F;dp&#x2F;1439800405&#x2F;ref=sr_1_7?ie=UTF8&amp;qid=1469389844&amp;sr=8-7&amp;keywords=ricardo+henry" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Modern-Introduction-Linear-Algebra&#x2F;dp...</a><p>[2] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Mathematics-Robert-Messer&#x2F;dp&#x2F;0065017285&#x2F;ref=sr_1_1?ie=UTF8&amp;qid=1469390271&amp;sr=8-1&amp;keywords=linear+algebra+gateway" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Mathematics-Robert-Mes...</a><p>[3] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Introduction-Mathematics-Undergraduate&#x2F;dp&#x2F;0387940995&#x2F;ref=sr_1_1?ie=UTF8&amp;qid=1469390501&amp;sr=8-1&amp;keywords=linear+algebra+valenza" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Linear-Algebra-Introduction-Mathemati...</a><p>[4] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Coding-Matrix-Algebra-Applications-Computer&#x2F;dp&#x2F;0615880991&#x2F;ref=sr_1_2?ie=UTF8&amp;qid=1469390643&amp;sr=8-2&amp;keywords=linear+algebra" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Coding-Matrix-Algebra-Applications-Co...</a><p>[5] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Algebra-Through-Geometry-Undergraduate-Mathematics&#x2F;dp&#x2F;0387975861&#x2F;ref=sr_1_1?ie=UTF8&amp;qid=1469390814&amp;sr=8-1&amp;keywords=linear+algebra+geometry" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Algebra-Through-Geometry-Undergraduat...</a><p>[6] <a href="https:&#x2F;&#x2F;www.amazon.com&#x2F;Advanced-Linear-Algebra-Graduate-Mathematics&#x2F;dp&#x2F;0387728287&#x2F;ref=sr_1_1?ie=UTF8&amp;qid=1469390934&amp;sr=8-1&amp;keywords=linear+algebra+roman" rel="nofollow">https:&#x2F;&#x2F;www.amazon.com&#x2F;Advanced-Linear-Algebra-Graduate-Math...</a>
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perseusprime11将近 9 年前
Higher Algebra by Hall and Knight