Lecture Time: Tuesday 13:00 - 15:35, and classroom B253 (=FEN-B1-K2-9).
See also the materials in THE SAKAI SYSTEM: https://online.deu.edu.tr/
The documents, review questions, worksheets, etc. for the course that I have given/assigned are the below files ordered by date.
Syllabus and the Bologna course catalogue for MAT5065 Advanced Linear Algebra
Some notes from the undergraduate linear algebra courses MAT2037 Linear Algebra I and MAT2038 Linear Algebra II may be useful for a review (unfortunately the university has ended the use of these personal web pages, I shall later produce a copy of these web pages).
But it is better having a fresh start from the following textbook that you shall study in the first half of the course:
Axler, S. Linear Algebra Done Right. Third edition. Springer, 2015.
Axler S. Linear Algebra Abridged. A free compactified version of Linear Algebra Done Right by excluding all proofs, examples, and exercises, along with most comments. This abridged version may be useful to review the main results in the textbook and it is a good exercise to prove the results in this abridged version without looking at the full book. It is free to download Linear Algebra Abridged.
Axler, S. Down with Determinants! American Mathematical Monthly 102 (1995), 139-154. The textbook is partly based on the ideas contained in this paper which received the Lester R. Ford Award for expository writing from the Mathematical Association of America. You can dowload the paper Down with Determinants!
Quizes, examinations and homeworks in the previous years 2018, 2019 and 2020 may be useful when studying:
One principle to be a problem solver is that you shall NEVER look for answers in the internet or some solution manuals to the above problems in your textbook or the above quiz, examination and homework examples. That is a skill that you must develop by concentrating on problems IF YOU WANT TO BE A MATHEMATICIAN AND TO MAKE RESEARCH TO ANSWER PROBLEMS NOT SOLVED ANYWHERE. Even the way to study your textbook must be to use the Abridged Version of Axler's textbook so that you must firstly attempt to prove every result in your textbook and only after you have proved, you must see the proof in the full textbook to check your proof and to see the details needed in a good writing of a proof. For the harder theorems, even if you cannot manage to completely prove, the effort you make will then be appreciated by you since only then you will be able to fully understand the important ideas needed to produce the proof.
After you have worked through the abridged and full versions of the textbook, it will be good to make a review of the textbook from the videos by the author:
Linear Algebra Done Right, Sheldon Axler, Videos
On thing that you shall use well without any problem is The Matrix of a Linear Transformation and the Change of Basis Formula.
In the lectures, we shall better use the notation in the following notes from the undergraduate linear algebra course for The Matrix of a Linear Transformation and the Change of Basis Formula. The main part of these lecture notes, the diagrams and matrices, have been typed in LaTeX by Yolay Akgün and edited by me, thanks to him. This notation is not the one in your textbook, but get used to this notation to keep change-of-basis calculus.
Lecture Notes following Axler's article
SPECTRAL THEOREM - Self adjoint, Unitary, Hermitian Matrices and Operators
Lecture Notes - SPECTRAL THEOREM - Self adjoint, Unitary, Hermitian Matrices and Operators
When studying determinants, it will be useful if you know well the sign of permutations in the symmetric group Sn, and even and odd permutations. See the notes The Sign of a Permutation by Keith Conrad (among the many nice Expository Papers).
You shall remember the geometric meaning of determinants from your multivariable calculus; in the Change of Variables Theorem for Multiple Integrals, Jacobian determinant enters the formula. For this viewpoint, see pages 88-130 for determinants from the recently published book Calculus and Analysis in Euclidean Space by Jerry Shurman whose web page also contains many nice notes which are useful for your other courses also. You shall like reading this book to learn rigorously and in a clean way main topics from advanced calculus.
For the first weeks, study firstly the four chapters on pages 1-130 from the texbook by Axler, solve all the problems there; be sure that you have no problem left in these introductory chapters. We shall have quiz and oral examinations from this part in the first few weeks of our term.
Below are the quizes, the midterm and final examinations: