This advanced textbook on linear algebra and geometry covers a wide range of classical of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. P. K. Suetin,Alexandra I. Kostrikin,Yu I Manin. This advanced textbook on linear algebra and geometry covers a wide range of of linear algebra with functional analysis, quantum mechanics and algebraic and differential geometry. P. K. Suetin, Alexandra I. Kostrikin, Yu I Manin. Gordon and Breach Science Publishers, – Algebras, Linear – pages Linear Algebra and Geometry · Alekseĭ Ivanovich Kostrikin,I͡U. I. Manin Snippet .
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If you want to have deeper insight in linear algebra with applications to geometry, I would suggest you to study the following advanced topics:. For this item, I have found an extremely good source, Multilinear Algebra and Applications.
Linear Algebra and Geometry – CRC Press Book
It will help you have a solid ground on linear algebra, being a quite nice book. I strongly reccomend you Naive Lie Theory. It is a must for someone wishing to relate linear algebra and geometry. Please read the article here and then try to read the first 20 pages of Spin Geometry. I think this is a good planning to study in summer. The references altebra nice and easily readable, but also having a higher level. For more on the geometry, take a look at Berger’s wonderful two-volume text Geometry.
It’s a very sophisticated treatment of classical geometries not differential geometryfull of linear algebra.
Text suggestion for linear algebra and geometry – Mathematics Stack Exchange
Allgebra might also look at Pedoe’s beautiful book, Geometry, A Comprehensive Coursewhich uses multilinear algebra as well as linear algebra.
There’s also the beginnings of Lie groups, so you could look at Curtis’s Matrix Groups. I spent nearly 3 years looking for an understanding as to how linear algebra related to geometry and how this approach was supposed to unify the subject, I have looked at every single one of the books mentioned here and none of them answered my question. Similarly chapters such as “Unitary Geometry” in Weyl’s ‘Group Theory and Quantum Mechanics’ would only lead one to push harder in finding some unified interpretation of linear algebra, so who wouldn’t want to check every good reference?
I’ve since found there is only a partial answer andd this question, and the answer is Gelfandonce you have general relativity and quantum mechanics to actually guide you into seeing this. You can basically view the first chapter on vector spaces and inner product spaces as developing a geometric formalism, modelled on putting a vector space into a curved space manifoldapplicable to general relativity geomeyry Euclidean geometry by extensionand the second chapter on operators and linear transformations as developing an algebraic formalism, modelled on complex numbers and polynomials which Axler also mentions, as I’m sure you’ve read mainly applicable to quantum mechanics remember QM is not going to demand pretty geometric interpretations!
Hence the importance of discarding the necessity for geometric interpretations here, and it unifies the subject when one does this!
In rough overview, in Ch. The very last section is on Hermitian geometry, i. Thus the picture is all motivated by imagining putting a vector tangent space to a curved manifold and invoking the equivalence principle locally. There is a similar way to naturally motivate all the Jordan normal forms, eigenvalues, adjoint, self-adjoint, normal, unitary etc Basically you can view sections from chapter 2 of Kostrikin as like a chapter 3 of Gelfand mixing your ideas together, or perhaps just extended versions of his section on bilinear forms.
As darij grinberg comments above, there’s Linear Algebra and Geometry by Suetin, Kostrikin, and Main it’s fairly difficult, but it should be accessible, given the time between now and when you originally asked this question. I didn’t read all of it, but quite liked what I did.
It has plenty of good exercises. On a different level entirely and not helpful for you, given that you’ve read Hubbard and Axler – I’m mostly putting this here in case someone else runs into this question is Ted Shifrin’s Linear Algebra: A Geometric Approach is a nice geometric approach to geometey algebra. It’s less abstract than the sources you give and covers far less ground than Shafarevich’s book doesbut offers a lot of geometric intuition.
He also prides himself on his exercises, in contrast to your experience with Shaferevich. It’s beautifully written, very careful and modern. It has probably the most detailed treatment of multilinear algebra you’ll find outside of a graduate algebra text. It may be a bit too difficult for your level, though. Check it out and judge for yourself. I’m happy to report there are several excellent advanced books on the subject now available from Dover.
A very good introduction to the geometry of linear algebra is Linear Algebra and Geometry: A Second Course by Irving Kaplansky.
This is a strongly rigorous and abstract treatment by one of the masters of algebra of the last century. I think you’ll find this book very helpful indeed. It’s considerably more difficult and specialized then Kaplansky, but I doubt you’ll find a deeper treatment of the connection between these 2 important subjects. Lastly, one of the most comprehensive treatments of mabin relationship between classical geometry and abstract algebra can be found in Groups and Symmetry by Paul Yale.
This is a surprisingly sophisticated treatment of not only groups of transformations,but the relations between rings and algebras and the classical transformations as well. A wonderful treatment you simply have to have kostrjkin there’s no good reason not to. It cannot be the main textbook for you, but seems to be a good source of exercises on the border of linear algebra and geometry, from near elementary to very advanced ones. I remember when I was in your situation trying to find the right source for good studying and intuitive thinking.
I recommend this MIT course with full video lectures, notes, problem sets, practice tests, and challenge problems the geomtery I personally like this course as a whole ane it develops you intuition over you reasoning, which is what a mathematician needs. In addition, I have also learned from this course about a six months or so ago and with full knowledge and understanding of the subject of mathematics.
I have done all the practice problems and even the challenging problems and that is what guided me through the course fast and efficiently.
Linear Algebra and Geometry
The course took me about a month or so to complete if you work really hard every day and constantly do problems so that the theorems and definitions just “stick.
It is actually a live online course that lets you interact with the community of other students in the program and the professors directing the course which to me is quite amazing. I would recommend that you begin this course after you have gone through half of the Algebda course.
However, no matter which one you choose, you will have a great experience with the concepts. In reference to learning geometry, I believe these course hold a firm foundation of high geometry.
If you take a look at them and experience the course yourself, you will understand. However, if you would like a supplementary source specific to geometry, I think that your current kostrikni have pretty good suggestions for that. The internet is full of many great sources that lonear can choose from. If you ever have trouble or find my resources not helpful I hope not!
Again, no matter what you choose from my “arsenal,” I bet that you will have a great intuitive experience with these sources. Also, it is always good to have more than one source when you are studying because you can compare geometfy contrast the ideas presented by each other resource.
I understand that you are higher level. So I would recommend clicking here. You will be able to learn analytic geometry along with linear algebra in the first result. In addition, I will say that there are over a million results. You will have many graduate and undergraduate courses gdometry lecture notes to work with to further you studies. If you have anymore questions, just feel free to email me.
Good luck with your studies! I thought that it would be better in a paragraph format for both of our benefit, as I wanted to write a lot to make sure that you understand where each source kostrikinn from and their format.
Home Questions Tags Users Unanswered. Text suggestion for linear algebra and geometry Ask Question. That text looks kostrukin. Does anyone have a similar suggestion that is less expensive or free? I found some answers to my question in answers to this post: You might find my answer to books about Linear algebra and geometric insight useful. If you want to have deeper insight in linear algebra with applications to geometry, I would suggest you to study the following advanced topics: Jjm 1, 9 Perhaps if you added a bit more focus to your question, we might be able to help kostrkkin a bit more.
Lectures in Abstract Algebra, vol 2. Linear Algebra and Differential Geometry.
Murtuza Vadharia 2 10 The third is what I was seeking an alternative to. Why do you recommend the first two? They read only what you put in geimetry title. I’ve noticed this a lot in my questions.
A bit different look, to build different intuitions: Uh-I think that’s not only too sophisticated for the reader’s level, but more then that,it’s only tangentially related to the subject matter requested. Julian Rachman 1, 9 The material you suggest is on the elementary level.
OP asks for more advanced texts and with connection to geometry. Please let me know why I got down voted. Finish 1, 8 Sign up or log in Sign up using Google. Sign up using Facebook.
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