What are good books for a third course in Linear Algebra?

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  • #1
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What are the suitable books in linear algebra for third course for self-study after reading Linear Algebra done right by Axler and Algebra by Artin?
 
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  • #2
S.G. Janssens
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Maybe you would like Roman's Advanced Linear Algebra.
 
  • #3
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But Roman omit some proofs. Is there any book more detail?
 
  • #4
What subject are you interested in? Ideas might be:
* Module theory
* Multilinear algebra
* Functional analysis
* Representation theory
* Numerical methods in linear algebra
If you've come this far, you'll know the field of 'linear algebra' is really a first-step towards each of the above, and they all offer different extensions. If you can be more specific people could recommend better books?
 
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  • #5
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I haven't had that knowledge. So I need a general book higher than Axler's book
 
  • #6
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Why make repeated threads? You asked about second course linear algebra books about a month ago. You are telling me you finished Artin and Axler in a month? Read what you have...
 
  • #7
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I have finished Axler, and I am reading Artin.I ask the question preparing for the time I finish Artin.
 
  • #8
Demystifier
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What are the suitable books in linear algebra for third course for self-study after reading Linear Algebra done right by Axler and Algebra by Artin?
Are you sure that you want a third book on linear algebra? Maybe you just want more advanced stuff on abstract algebra, not necessarily linear.
 
  • #9
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I need to go deeper in Linear Algebra
 
  • #10
S.G. Janssens
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I need to go deeper in Linear Algebra
Need or want?

Both is fine, linear algebra is alive as a research field by itself, not only as background knowledge for other fields. (Although its connection with other fields makes it arguably more interesting.)

Maybe try browsing and reading some articles. This is freely accessible:

https://journals.uwyo.edu/index.php/ela

zbMATH curates a searchable journal list that is free to consult.
 
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  • #11
StoneTemplePython
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I haven't had that knowledge. So I need a general book higher than Axler's book
You are asking for a book after Artin and Artin has two very nice chapters on Module Theory and Representation theory respectively so this comment doesn't make much sense.

Btw, if you want more comprehensive knowledge an easy upgrade is to do the (especially starred) problems in Artin 1st ed. He dumbed down the problems in the 2nd edition -- i.e. cut down the raw number and eliminated a lot of high insight but difficult problems.
 
  • #12
Infrared
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I need to go deeper in Linear Algebra

Why? Are there specific topics that you want to learn about?
 
  • #13
martinbn
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Kostrikin and Manin "Linear algebra and geometry".
 
  • #14
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I have finished Axler, and I am reading Artin.I ask the question preparing for the time I finish Artin.
... in which case it shouldn't be a problem to answer ...
Why? Are there specific topics that you want to learn about?
... because ...
I need to go deeper in Linear Algebra
... requires specific topics that you call deeper, in order to make specific suggestions.
 
  • #15
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Some online University teach PhD on Linear Algebra, so I need a deeper in general Linear Algebra
 
  • #16
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Let me see where you are. Maybe this helps us to figure out what you should do.

Let ##\psi## be a linear transformation of the inner product space ##E##. Define the linear automorphism ##\exp \psi## by
$$
\exp\psi =\varphi (1)
$$
where ##\varphi (t)## is the family of linear automorphisms defined by
$$
\dot\varphi (t)=\psi\circ \varphi (t)\, , \,\varphi (0)=\operatorname{id}.
$$
Prove that
$$
\varphi (t)=\exp(t\psi) \quad (-\infty <t<\infty ).
$$

https://www.amazon.com/dp/0387901108/?tag=pfamazon01-20
p. 258
 
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  • #17
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I have not finished undergraduate in math(self-study).I have just only read Basic Analysis by Peterson Vol 1-3 and Linear Algebra done right by Axler and preparing to read Algebra by Artin.So I haven't been able to solve problem in Greub.Is it good to read Greub after finish Artin?
 
  • #18
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I have not finished undergraduate in math(self-study).I have just only read Basic Analysis by Peterson Vol 1-3 and Linear Algebra done right by Axler and preparing to read Algebra by Artin.So I haven't been able to solve problem in Greub.Is it good to read Greub after finish Artin?
By read, do you mean working through the exercises without looking at solutions?
 
  • #19
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I intent to do exercices after re-reading the books. I like have a general view about mathematics.
 
  • #20
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I intent to do exercices after re-reading the books. I like have a general view about mathematics.
Thats not how science or math books works. You have to do the exercises...
 
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  • #21
Vanadium 50
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I intent to do exercices after re-reading the books.
This explains why you have posted so many messages struggling with various things. @MidgetDwarf is right.
 
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  • #22
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So I haven't been able to solve problem in Greub.Is it good to read Greub after finish Artin?
Sure, Greub is a good book. But it will not solve your problem. You can read a thousand books and still don't make a progress. Those books you already have are good books, too, and working through them should qualify you to solve most linear algebra problems.

The key attitude when reading a scientific book is: "I do not believe any of what is written! Book, convince me!"

E.g. a rotation is a linear transformation. Then you have to think that it is not, but the book or your personal work makes you see that it is one. What does it mean, that it is linear? Can I draw a picture? Why does it have those properties? Is it correct under any circumstances, or are there exceptions? These kinds of questions, a pencil and a lot of paper to scribble on must be present all the time when you read a textbook.
 
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  • #23
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Yes,you are right! And I need every thing must be "demonstrated" .I have spirit "must be convinced by logic".But I want save time not to do exercices at first time.And in short time I have general view about Math.
Is that way OK?
 
  • #24
berkeman
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Yes,you are right! And I need every thing must be "demonstrated" .I have spirit "must be convinced by logic".But I want save time not to do exercices at first time.And in short time I have general view about Math.
Is that way OK?
IMO, No. If you work through a chapter in a textbook and skip the exercises, you are wasting your time (and ours, BTW) if you want to be sure you are effectively learning the material. The exercises are a test of your understanding. "Self Learning" does not mean that you get to skip the learning part and just get a general idea of the material.

How about we pause this thread until you go back and re-read your first couple of textbooks and work through the exercises. When you can show us the solution to the straightforward math quiz question posed by @fresh_42 we can resume this discussion thread...
 
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  • #25
Demystifier
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Yes,you are right! And I need every thing must be "demonstrated" .I have spirit "must be convinced by logic".But I want save time not to do exercices at first time.And in short time I have general view about Math.
Is that way OK?
I understand why others criticize you, but I have to tell you that I use similar strategy when I only want to get a big picture in a short time. After getting a big picture, then I can more easily motivate myself to study the details. So if that strategy works for you too (obviously, it doesn't work for everybody), go with it!
 

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