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I came to know about Gilbert Strang's two books, "Introduction to Linear Algebra" and "Linear Algebra and its Applications". The first is the one used as the text in the 18.06 linear algebra MIT course. I have almost all the videos of 18.06 which deal with basics linear algebra (like left out the portions of Markov matrices, differential equations, Fourier series, etc). Though Gilbert Strang's videos are awesome and highly intuitive, it does not define many things, from which I have encountered questions like: Block determinants, rank, nullity theorem, the general form of the characteristic equation (using the concept that rth co-efficient is the sum of the principal minors of order r), principal minors, and many other small pieces which can be used to answer MCQ question in competitive examinations.

Though the second book, has concepts like rank, nullity, etc, but even there, many concepts which I need are missing, and it is more inclined towards application stuff.

Please can anyone recommend me an intuitive yet comprehensive and easily readable (student-friendly) book on Linear Algebra which do not focus much on applications, just basics

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    $\begingroup$ Search terms: OER (open educational resources), creative commons $\endgroup$
    – Sue VanHattum
    Jun 20 at 23:19
  • $\begingroup$ Where to incorporate these search terms? $\endgroup$ Jun 21 at 6:56
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    $\begingroup$ google (I did a search a found lots of free books.) $\endgroup$
    – Sue VanHattum
    Jun 21 at 15:24
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    $\begingroup$ This doesn't really count as a book, but maybe consider Evan Chen's Napkin document. Evan is highly involved in the USAMO and so has a perspective on competition math. $\endgroup$
    – Steve
    Jun 21 at 17:25
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    $\begingroup$ My non-constructive comment is to agree that Strang is overrated, and his books are poorly structured. I suppose they are a direct recording of his lectures with missing definitions, explanations and generally jumping around instead of having a consistent course. $\endgroup$
    – Rusty Core
    Jun 21 at 19:14
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Despite the last word in the name, you might consider Bernard Kolman's Linear Algebra with Applications. Most of it is not applications and you can ignore the parts that are (tending to be at the ends of chapters or exercise sessions), and just get help with the basics.

FWIW, I find it incredibly easy and gentle. Almost entirely requires no calculus, for instance. Will get you comfortable with the basic terms/concepts in "mattress theory" before moving on to those tougher books that all the smart people on the Internets push.

It's an older book--I have 3rd edition, 1984. You should be able to get a cheap copy from a used bookseller.

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Perhaps take a look at "Linear Algebra Done Wrong" by Treil. Free PDF download, so you can take a thorough look. Others swear by Axler's "Linear Algebra Done Right", to which the previous is a reaction, but this one isn't available for free.

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Finite Dimensional Vector Spaces by Halmos is worth the read. This was picked up by Dover and a physical copy should be relatively inexpensive.

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