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August 18th, 2016, 06:55 AM   #1
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Any Good Books?

Good evening!

I'm trying to find a good book about linear algebra, but I don't know how to judge a book for mathematics, so I was wondering if I could have some help.

I wish for a book that refers to newbies about linear algebra (of course, I already possess basic algebra knowledge from high school).

Also, if possible, I'd like it to be translated into the Greek language.

My math skills are algebra and infinitesimal calculus, but I'm a newbie in linear algebra. Unfortunately, I have "knowledge gaps" in trigonometry and Geometry.

The higher amount I would like to pay is 60 Euros (or dollars).

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Last edited by skipjack; August 18th, 2016 at 09:34 AM.
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August 18th, 2016, 07:07 AM   #2
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Most books concentrate on one part of Linear Algebra or another - it is a very wide subject.

For most people this is the best overall book.

https://www.amazon.co.uk/Elementary-.../dp/0470432055

Note that there are many editions and two versions.
One version is called the applications version and, as suggested, has lots of extra applications.

You do not need the latest (and most expensive) editions a second hand copy of an earlier edition is just fine and much cheaper.

Anton develops all the necessary additional maths so you need not worry about your gaps.

The other book worth having is

https://www.google.co.uk/search?q=+k...90.ynSPN59AZOY

Linear analysis is a different subject from linear algebra, though the techniques are much the same.

Again older editions can be had cheaply or even pdfs
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August 18th, 2016, 09:47 AM   #3
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I think this one will do like a charm!
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August 18th, 2016, 09:59 AM   #4
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A web search suggests that Strang's book, Linear Algebra and its Applications (ISBN 978-0534422004) might also be useful as there are online lectures that relate to it.
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August 18th, 2016, 10:38 AM   #5
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Strang's book is excellent but you need some more advanced maths than the OP has.

I had Strang, Nering, Hoffman and Kunze and the two I mentioned.
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August 19th, 2016, 08:33 AM   #6
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Quote:
Originally Posted by skipjack View Post
A web search suggests that Strang's book, Linear Algebra and its Applications (ISBN 978-0534422004) might also be useful as there are online lectures that relate to it.
Does this book contains theory or only exercises? I did a search on google
and i was only getting exercises about linear algebra not theory.
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August 19th, 2016, 09:30 AM   #7
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Quote:
Does this book contains theory or only exercises? I did a search on google
and i was only getting exercises about linear algebra not theory.
It depends on why you want to study linear algebra.

Each book has a different perspective on linear algebra.

Linear algebra is part of abstract algebra so if you want to study formal linear algebra in the context of higher formal algebra then you need Nering or Hoffman and Kunze.
They are, however very dry and hardly go in for worked examples.
Just the old fashioned axioms, lemma; theorem and proposition style, repeated over and over with proper formal proofs.
Detailed explanation is in short supply; you have to work all this out for yourself.

Strang, Anton and Kreider are about applications of the subject.
They are all well supplied with worked examples as well as exercises.

Strang concentrates on matrix theory and methods of manipulating them and the data they contain, particularly for solving simultaneous equations.
Theory pertinent to this aim is presented.

Anton has a wider brief for instance look at page 330 in the version you referenced.
He does treat simultaneous equations but is more interested in linear algebra from the point of view of coordinate systems.

He discusses the incredibly important vector space axioms there, a subject not properly treated in Strang.

Kreider etc also treats vector space axioms well, but differently since their treatment spans most of engineering maths - linear differential equations, recurrence equations, laplace transforms, as well as the applications to coordinate systems and matrices.

Does this help?

Last edited by skipjack; August 20th, 2016 at 09:04 AM.
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August 20th, 2016, 07:48 AM   #8
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So many subjects!!! I actually want to learn the basics of linear algebra. And yes, I think
the book must focus on matrix, because our professor actually was teaching us matrix
the entire year and he was very strict on how to use them in real applications (mostly in computer graphics, because I'm studying for electronic computer engineering, not a mathematician). For example one of his favorite exercises is how to use a matrix to spin (in
angles) vectors but it's not actually an exercise, it's an application where you must figure out how to use spin matrix to solve the problem.

Last edited by skipjack; August 20th, 2016 at 09:05 AM.
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August 20th, 2016, 09:01 AM   #9
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Quote:
(mostly in computer graphics, because I'm studying for electronic computer engineering, not a mathematician).
In which case Anton and perhaps Kreider maybe plus a decent engineering maths book and a discrete maths book are all you need.
Strang will not be very useful to you.

Methods heavily used in electrical/electronic engineering such as Fast Fourier Transforms, Digital Filter maths etc are treated better in dedicated electrical engineering books.

Spatial manipulation is also better treated in specialist books on computational geometry.

Computational geometry of Spatial Forms

Gasson

Computational Geometry for Design and Manufacture

Faux and Gasson

The Mathematical Description of Shape and Form

Lord and Wilson
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Last edited by skipjack; August 20th, 2016 at 09:08 AM.
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August 20th, 2016, 09:12 AM   #10
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Your professor should be able to provide a list of recommended books. Even if they are expensive, it should be easy to sell them if they're on such a list.
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