- #1

- 323

- 15

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?

Last edited:

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Linear Algebra
- Thread starter fxdung
- Start date

- #1

- 323

- 15

Last edited:

- #2

S.G. Janssens

Science Advisor

Education Advisor

- 958

- 728

Maybe you would like Roman's Advanced Linear Algebra.

- #3

- 323

- 15

But Roman omit some proofs. Is there any book more detail?

- #4

- 6

- 3

* 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?

- #5

- 323

- 15

I haven't had that knowledge. So I need a general book higher than Axler's book

- #6

- 1,142

- 317

- #7

- 323

- 15

- #8

- 11,762

- 4,198

Are you sure that you want a third book on

- #9

- 323

- 15

I need to go deeper in Linear Algebra

- #10

S.G. Janssens

Science Advisor

Education Advisor

- 958

- 728

Need or want?I need to go deeper in Linear Algebra

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.

- #11

StoneTemplePython

Science Advisor

Gold Member

- 1,188

- 584

You are asking for a bookI haven't had that knowledge. So I need a general book higher than Axler's book

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

Science Advisor

Gold Member

- 915

- 507

I need to go deeper in Linear Algebra

Why? Are there specific topics that you want to learn about?

- #13

martinbn

Science Advisor

- 2,283

- 782

Kostrikin and Manin "Linear algebra and geometry".

- #14

fresh_42

Mentor

- 14,892

- 12,445

... in which case it shouldn't be a problem to answer ...

... because ...Why? Are there specific topics that you want to learn about?

... requires specific topics that you call deeper, in order to make specific suggestions.I need to go deeper in Linear Algebra

- #15

- 323

- 15

Some online University teach PhD on Linear Algebra, so I need a deeper in general Linear Algebra

- #16

fresh_42

Mentor

- 14,892

- 12,445

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

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

Last edited:

- #17

- 323

- 15

- #18

- 1,142

- 317

By read, do you mean working through the exercises without looking at solutions?

- #19

- 323

- 15

I intent to do exercices after re-reading the books. I like have a general view about mathematics.

- #20

- 1,142

- 317

Thats not how science or math books works. You have to do the exercises...I intent to do exercices after re-reading the books. I like have a general view about mathematics.

- #21

Vanadium 50

Staff Emeritus

Science Advisor

Education Advisor

- 27,002

- 10,835

This explains why you have posted so many messages struggling with various things. @MidgetDwarf is right.I intent to do exercices after re-reading the books.

- #22

fresh_42

Mentor

- 14,892

- 12,445

Sure, Greub is a good book. But it will not solve your problem. You canSo I haven't been able to solve problem in Greub.Is it good to read Greub after finish Artin?

The key attitude when

E.g. a rotation is a linear transformation. Then you have to think that it is not, but the book

- #23

- 323

- 15

Is that way OK?

- #24

berkeman

Mentor

- 59,700

- 9,850

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.

Is that way OK?

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...

- #25

- 11,762

- 4,198

I understand why others criticize you, but I have to tell you that I use similar strategy when I

Is that way OK?

Share:

- Replies
- 1

- Views
- 182

- Replies
- 7

- Views
- 5K

A