What can I expect from a course in Abstract Linear Algebra?

In summary, the course Abstract Linear Algebra may involve some computations in the midterm, but it is primarily focused on proofs and abstract versions of linear transformations, rather than using matrices and determinants. If you want a better understanding of this concept, you can refer to the book Linear Algebra Done Right by Sheldon Axler.
  • #1
JasonRox
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What should I expect out of a course named Abstract Linear Algebra?

I have just taken two courses on Linear Algebra, and it was mainly computational.

I was hoping that this course would not involve any computations, but the professor says we will have some (how much?) on our next midterm.

I don't mind having them for assignments, and as for examples, but on the midterm?

After doing annoying computations for two terms, I certainly don't want to continue doing them. Is it expected to continue doing computations in Abstract Linear Algebra?

Note: We still have questions like find a basis for V (a vector space).
 
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  • #2
look at my notes on my web page for linear algebra. that's probably considered abstract linear algebra by some people, although i myself just consider it linear algebra.

http://www.math.uga.edu/~roy/

i would guess people mean vector spaces and linear maps as abstract linear algebra, and matrices as concrete linear algebra (I was tempted to say stupid linear algebra, but i won't)..
 
  • #3
mathwonk said:
look at my notes on my web page for linear algebra. that's probably considered abstract linear algebra by some people, although i myself just consider it linear algebra.

http://www.math.uga.edu/~roy/

i would guess people mean vector spaces and linear maps as abstract linear algebra, and matrices as concrete linear algebra (I was tempted to say stupid linear algebra, but i won't)..

Well, on our midterm we will be expected to construct matrix transformations for any given transformation.

I really hate doing that. I really really really do.
 
  • #4
Abstract linear algebra probably means little or no use of matrices at all as well as not doing any determinants. everything will be proofs and instead of matrices you will be using the abstract version of a linear transformation much more. if you have a chance, look at Linear Algebra Done Right by Sheldon Axler (you can look at it on amazon). His book is pretty much just a pure abstract treatment of linear algebra.
 

1. What is abstract linear algebra?

Abstract linear algebra is a branch of mathematics that deals with vector spaces and linear transformations in an abstract setting. It focuses on the fundamental concepts and properties of vectors and linear transformations, rather than specific applications or computations.

2. What are the key concepts in abstract linear algebra?

Some key concepts in abstract linear algebra include vector spaces, linear independence, basis and dimension, linear transformations, eigenvectors and eigenvalues, and inner product spaces.

3. How is abstract linear algebra different from traditional linear algebra?

Traditional linear algebra typically deals with specific vector spaces, such as Euclidean spaces, and focuses on solving systems of linear equations and performing computations. Abstract linear algebra, on the other hand, is more general and deals with vector spaces and linear transformations in an abstract and theoretical manner.

4. What are the applications of abstract linear algebra?

Abstract linear algebra has various applications in fields such as physics, engineering, computer science, and economics. It is used to model and analyze systems that exhibit linear behavior, such as circuits, control systems, and optimization problems.

5. What are some useful resources for learning abstract linear algebra?

There are many textbooks and online resources available for learning abstract linear algebra. Some popular textbooks include "Linear Algebra: A Modern Introduction" by David Poole and "Linear Algebra Done Right" by Sheldon Axler. Online resources such as Khan Academy and MIT OpenCourseWare also offer free courses and lectures on abstract linear algebra.

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