Linear Algebra 1&2 (88/89-112/3)
Linear Algebra 1&2 (88/89-112/3)
Supplement materials:
Link to a site of a similar course Linear Algebra 1 (by Prof. R. Adin). Note: the site's Hebrew text is corrupted, but on the right there is a menu where you can view excellent lecture notes.
For Linear Algebra 2: Notes by Ed Nelson on the proof of Jordan normal form (and another site on related issues).
Bibliography:
Recommendations for more advanced text books (with their library codes):
S. Lang, Linear algebra, 15-01LAN -- a very clear exposition;
G. Mostow et all, Fundamental linear algebra, 15-01MOS;
Hoffman&Kunze, Linear algebra, 15-01HOF - the classic;
Shilov, Linear algebra, 15-01SHI (exists in Russian too);
Halmos, Finite-dimensional vector spaces, 15-02HAL - essentially a collection of problems; highly recommended!
Roman, Advanced linear algebra, 15-02ROM - an advanced book for the second reading;
In Hebrew: ש. עמיצור, אלגברה א. ,15-01עמיאל -- quite algebraic, but highly recommended.
As a preparation for the exam in Linear Algebra 1, it is recommended that you know instant solutions to the following problems from Prof. B. Tsaban's book (6th edition):
From Chapter 1 on Fields: 3.1, 3.5, 4.1, 4.2;
From Chapter 2 on Linear systems: 1.2, 1.7, 1.8;
From Chapter 3 on Matrices: 3.3, 3.4, 3.6, 4.2, 5.10, 5.11, 6.1, 6.2, 6.9, 6.10, 6.11, 6.18;
From Chapter 4 on Vector spaces: 1.3(=2.5+1/2), 1.4, 1.5, 2.5, 4.1, 4.4, 4.6, 5.5, 5.6, 5.7, 6.2, 6.4, 7.1, 7.6, 7.17, 8.1, 8.5, 10.5, 11.6, 11.8, 11.13.
From Chapter 5 on Linear Maps: 2.3, 2.5, 2.6, 2.7, 2.9, 2.16;
To check your skills try to solve 2.18, 2.19, 2.20 (these are exam level problems);
3.12, 3.13, 3,20, 4,15,4.21, 4.22, 4.65, 4.86, 5.16, 5.22, 5.28, 5.29, 5.30, 5.36, 5.44, 5.50, 5.51, 5.53, 5.54, 5.55, 5. 58, 5.59 :( ליפשוץ (מהדורה שניה 1993
As a preparation for the exam in Linear Algebra 2, it is recommended that you know instant solutions to the following problems from Prof. B. Tsaban's book (6th edition):
From Chapter 7 on Eigenvectors: 1.8, 1.15, 1.18, 1.20, 3.13, 5.22;
From Chapter 8 on Inner spaces: 4.19, 5.6, 5.7, 5.12;
From Chapter 10 on Adjoint maps: 1.7, 2.9, 2.12, 3.23; To check your skills try to solve 3.8.
Past Exams:
Solution to the 2015a exam in Linear Algebra 1.
Solution to the 2014a exam in Linear Algebra 1.
Solution to the 2013a exam in Linear Algebra 1.
Solution to the 2011 exam in Linear Algebra 1.
Solution to the 2007-A exam on Linear algebra 1 (88-112). Exam 2007-A.
Solution to the 2010 exam in Linear Algebra 2.
Linear algebra 2 (88-113) Exam 2009-A.
A sample of a midterm Quiz in Linear Algebra 1.
A sample of a midterm Quiz in Linear Algebra 2. Solution.
Solution to the 2012-B exam in Linear algebra 2 (88-113)