# What books to read for learning linear algebra?

Hi!
I would like to reach an understanding of neural networks and start to work with it. Read a couple articles, watched a couple of videos on this topic. I realized that I need maths, and in particular linear algebra.

The last time I studied algebra in the 11th grade (my UNIVERSITY was not technical and higher mathematics was only on 1 course, but I remember that the matrix was held and only)
Advise the books to study linear algebra in Russian or in English.
Thanks for the replies!
June 8th 19 at 17:11
June 8th 19 at 17:13
Il'in V. A. G. D. Kim, Linear algebra and analytical geometry.
June 8th 19 at 17:15
Before we look at the line you want to develop other sections of algebra. So I recommend this book (there is everything you need):
D. K. Faddeev, Lectures on algebra. M.: Nauka, 1984.
This is what other topics you want to study and why? I disagree. - Ernestina.Dibbe commented on June 8th 19 at 17:18
It does not matter what "dissent".

Here, for starters, the definition of vector (linear) space:
A vector space S over a field K is called additively written Abelian group, elements which define the action of multiplication by elements of a field K, satisfying the requirements:
a(x + y) = ax + ay,
(a + b)x = ax + bx,
a(bx) = (ab)x,
1•x = x,
where a, b, 1 - a elements of the field K, x, y - elements of a vector space.

And this is the beginning - definition. Then think for yourself. - Domingo.Keeling11 commented on June 8th 19 at 17:21
What? Neither theory of groups nor a specific theory of Abelian groups or the theory of meaningful fields in the standard course of linear algebra not applicable not monocyte head. - Ernestina.Dibbe commented on June 8th 19 at 17:24
And to study neural networks you don't need that, at least in the first place (unlike analysis). - Ernestina.Dibbe commented on June 8th 19 at 17:27
Stop giving me the runaround. For many years I have taught range in relevant College programs (all algebra for 1-3 semesters).

TS asked what to read on the line, but not on neural networks.

He even determine you do not understand, if she doesn't know started group theory (definition and elementary properties; what you need to know the theory of the groups in the amount of, for example, a 3-semester math major, I did not say - learn to read and understand what others have written); the same applies to the beginnings of field theory. In addition, it is necessary to know complex numbers and theory of polynomials.

The fact that the algebra course (with some variations) is read in sequence - it's not from the bulldozer, and based on the fact that the material of the 1st semester is necessary to understand line. - Domingo.Keeling11 commented on June 8th 19 at 17:30
I also taught.

TS asked what to read in linear algebra for neural networks (this is the question about the ability to read). So, for example, the nuances associated with the zero characteristic can safely ignore it.

In the above definition can be replaced by the word "additively written Abelian groups" on the axioms of an Abelian group and not lost anything. So, in fact, often do. For example, see a wonderful tutorial Gelfand (which I recommend TS). Group theory is not needed in any amount. And about the fields don't need to know anything, even the definition is not necessary: you can do everything over the real and complex numbers (again, for neural networks, nothing else is needed). And about complex numbers and polynomials (in the volume of additions-multiplications, and not the "basic theory"), the graduate school, maybe, knows. - Ernestina.Dibbe commented on June 8th 19 at 17:33
TC:
Advise the books to study linear algebra in Russian or in English.

And what he needs for neural networks - let alone understands.
In the above definition can be replaced by the word "additively written Abelian groups" on the axioms of an Abelian group and not lost anything.

Will not be lost. Only skills of work with such objects (simpler than the PL) he will not. It is not in the replacement of some words to others, and in fact.
For example, see a wonderful tutorial Gelfand (which I recommend TS).

The tutorial is good, only there is some non-standard definition (he identifies vector space and affine space that should not be done and can fool the reader who is not familiar with this feature).
Group theory is not needed in any amount.

Cm. above.
And about the fields don't need to know anything, even the definition is not necessary: you can do everything over the real and complex numbers

Yeah, two different definitions of VP - one for R, the second for C.

And about complex numbers and polynomials (in the volume of additions-multiplications, and not the "basic theory"), the graduate school, maybe, knows.

First, don't know. It is not included in the school curriculum (I knew from school, but went to matelasse and it was in the 70s; what could be in the modern school complex numbers, if current students have problems with addition of fractions). And it is not "in the volume of additions-multiplications", and the basics necessary to know, otherwise there will arise problems with characteristic polynomials of its own numbers, INF etc. (the algebraic closure of C, etc). - Domingo.Keeling11 commented on June 8th 19 at 17:36
> And what he needs for neural networks - let alone understands.

Or I it prompt. To -- the context.

> Can't lose. Only skills of work with such objects (simpler than the PL) he will not.

It is not required neither in your interpretation of the question, nor mine.

> Yeah, two different definitions of VP - one for R, the second for C.

Gelfand so. And no one died! He still, however, in passing to notice that everything more or less works for any field, but could not see how do not notice many other books.

By the way, what you taught "profile preferences" do not strengthen, and weakens the argument. It is clear that it is appropriate to say about the group and about the ring is a principal ideal if it's still to explore, it's not the focus. Now, if your arena had, on the contrary, run-down Economics University, and still without the words "group" and "field" well, they failed to do, it would be brighter. But it would not be true. In textbooks on linear algebra, aimed not at specialists in technical and engineering disciplines, have to do without. Often, the minimum required information on the polynomials or is there complex numbers in them can also be found. By the way, I studied them in school (with a regular program in mathematics and much later than the 70s). As for the fact that some students problems with common fractions, then in the 70s and not all mastered everything he was supposed to. This is a separate issue.

Itoga: "other sections of algebra" even in the volume of an introductory textbook Faddeev did not need to study linear algebra. - Ernestina.Dibbe commented on June 8th 19 at 17:39
,
It is not required neither in your interpretation of the question, nor mine.

Wrong.
Gelfand so.

Wrong.
It is clear that it is appropriate to say about the group and about the ring is a principal ideal if it's still to explore, it's not the focus.

Good list. First - the basis for all (mathematical specialty, but not only her), the second - only of course on commutative (also read not just students), which is not for everyone for sure.
By the way, I studied them in school (with a regular program in mathematics and much later than the 70s).

This is nonsense, since neither that, nor another is not included in the school curriculum: a complex number of the word at all, polynomials - there is generally a pathetic stub type square trinomial, etc.. You are all in the textbooks-have a look on algebra. If you have a teacher took the initiative, he could squeal on the head in the area if this was not in matclass.
As for the fact that some students problems with common fractions, then in the 70s and not all mastered everything he was supposed to.

Not all of them. But just for the entrance exam to the Mat. the faculty 15 years ago to ask one more question on addition of fractions - it was the coup de grâce to already sure issues do not arise, the person may or may not learn at the faculty, in recent years this issue has become too dangerous to ask can the group not to score. I watched it personally for more than a quarter of a century.
Itoga: "other sections of algebra" even in the volume of an introductory textbook Faddeev did not need to study linear algebra.

Itoga: other sections of the algebra in the partial volume of an introductory textbook Faddeev (specifically under the line it is necessary to choose the right part) is absolutely necessary to study linear algebra (to the actual line he separately deals with matrices and determinants and forms that absolutely must have). - Domingo.Keeling11 commented on June 8th 19 at 17:42
thanks for the answers , but alternative point of view from me would be better.
I'd like to know anything that even indirectly relates to the topic of study in neural networks and other disciplines, but my experience and intuition tell me that the correct solution to my question will be the textbook by Gelfand and I do not exclude that this decision will have a negative result. But I can handle it, perhaps with the help of the Faddeev tutorial :)

thank you for the responses, your point of view was more convincing. Please, if you have something to add or give advice I would be glad to listen.

Once again thank you all :) - harmon.Koelpin commented on June 8th 19 at 17:45
, matrices and determinants I refer to linear algebra. As for the rest of your remarks, I disagree, but to argue no more. - Ernestina.Dibbe commented on June 8th 19 at 17:48
on the Styopik there is a course in neural networks, begins with literacy classes for linear algebra: https://stepik.org/course/401/syllabus. - Ernestina.Dibbe commented on June 8th 19 at 17:51
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thanks for the answers, but alternative point of view from myrslok suits me more.

If you knew, what is more, you wouldn't need to ask your question.

When you hit that don't know what you need to know to understand the product line (and this necessarily happens), you can ask me what to read from the same Faddeev.
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matrices and determinants I refer to linear algebra.

There are different approaches. This is the most common. Although, for example, Kostrikina in his books a different approach. - Domingo.Keeling11 commented on June 8th 19 at 17:54

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