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Linear algebra from ground up?

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Can anybody recommend a beginner's book on linear algebra? I read the old "EPR" paper and I want to learn that maths. Hilbert spaces, eigenfunctions, that sort of stuff.

I've tried a couple but right at the start there's some leaps of logic I just can't seem to get my heads around lol. Is there a "go-to" textbook that excels at teaching this stuff?

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I would start with an average High School Algebra book.  Pearson and a number of other textbook publishers make very good ones.  They tend to be aimed at a population of students that have a wide range of learning styles, so they have written material, pictures, examples and other such things.   Once you know what learning style fits you best you can then move on to more tailored textbooks.  There are more modern teaching systems, such as "Eureka Math" but they do not have well-developed reading material and tend to be more narrow in the learning styles they address.   I've taught Algebra using the older books and with Eureka Math, but the older books seem to have broader success.

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The best book for your purpose is Elementary Linear Algebra by Howard Anton.

There are several versions

The basic one and the expanded one called the applications version or with applications.
There are also complete solutions manuals to the exercises.

I think they are up to the 11th edition now, but any edition is fine and you can get some very cheaply second hand.

 

Beware that many 'linear algebra' books were written mostly to teach the solution of sets of linear equations and not much else.
These will not suit you.

 

Othere books are probably too advanced eg

Nering

Hoffman and Kunze.

 

Linear Algebra is a very wide field so come back and ask again when you have grabbed the basics and have a better idea what you what to do with them.

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