Administrative Matters
(Click
here
for the Hebrew version.)
SYLLABUS:
1. Fields; the field of complex numbers.
2. Systems of linear equations; the algebra of matrices.
3. Vector spaces and linear transformations.
4. Determinants and volumes.
5. Spectral theory: eigenvalues and eigenvectors.
6. Inner product spaces.
Exercise sheets will be posted regularly.
The FINAL GRADE in the course will be calculated as follows:
the worse of the two midterm tests: 5%,
the better of the two midterm tests: 20%,
final exam: 75%.
The midterm tests will take place on Friday 05.12.2014 and Friday 09.01.2015 (NOTICE THE NEW DATE!).
If you cannot or could not attend one of the midterms due to a justified reason
(reserve service, hospitalization, time conflict with another test),
please notify your lecturer at once.
The grade of the missing midterm will be replaced by the grade of the final exam.
Grades of the First Midterm,
Grades of the Second Midterm
SELECTED BIBLIOGRAPHY:
Kenneth Hoffman, Ray Kunze. Linear Algebra. 1971 (2nd edition), English.
Amnon Yekutieli. Introduction to Linear Algebra. Hebrew.
Seymour Lipschutz. Linear Algebra.
Schaum's Outline Series, 1991 (2nd edition), English; 1993, Hebrew translation.
Lecturers:
Prof. Gregory Mashevitsky
(phone: 08-647-7803)
Sunday 17:10-18:10, Wednesday 15:10-16:10 (Room 304, Building 58).
Dr. Eliyahu Matzri
(phone: 08-647-7812)
Wednesday 11-13 (Room 125, Building 58).
Dr. Eitan Sayag
(phone: 08-647-2713)
Tuesday 16-18 (Room 107, Building 58).
Prof. Victor Vinnikov
(phone: 08-646-1618)
Monday 15-17 (Room 103, Building 58).
Teaching Assistants:
Hezi Halawi
Thursday 14-16 (Room -120, Building 59).
Nadav Meir
Tuesday 18:10-19:00 (Room 204, Building 97), Thursday 13:10-14:00 (Room -120, Building 58).
Amit Shomrat
Sunday 15-16, Monday 13-14 (Room -127, Building 58.
Yakim Silverman
Monday 16-17, Tuesday 9-10 (Room -120, Building 58).
Practice Homework No. 1 (review of some background material)
Practice Homework No. 2 (fields, the field of complex numbers; there are some corrections in red)
Practice Homework No. 3 (linear systems; there are some corrections in red)
Practice Homework No. 4 (matrix algebra)
Practice Homework No. 5 (vector spaces: linear combinations, span)
Practice Homework No. 6 (vector spaces: linear independence, bases, dimension)
Part A,
Part B
Correction: Part B, Problem 7a: there is no connection between the subspace V that you are required to find here
and the subspace V that was defined on the line above.
Practice Homework No. 7 (linear transformations: the kernel and the image)
Practice Homework No. 8 (linear transformations: the representing matrix, the algebra of linear transformations)
Corrections: Problem 9b: should be dim Im T^n = dim Im T^{n+1} (Im is missing).
Problem 10: should be Ker T contains Span{e_1,e_2}
and Im T is contained in Span{e_3,e_4} (containment instead of equality).
Practice Homework No. 9 (determinants)
Practice Homework No. 10 (eigenvalues and eigenvectors, diagonalization)
Notice the correction in Problem 10 (there is no sign (-1)^n).
Practice Homework No. 11 (inner product spaces)
Practice Homework No. 12 (operators on inner product spaces)
Additional Problems,
Problems on Matrix Decompositions
NOTICE: Solutions to many of the problems are available at the course moodle site.
The first midterm test will take place on Friday, 05.12.2014.
Material to be covered: fields (including the field complex numbers), systems of linear equations,
the algebra of matrices, definition and basic properties of vector spaces (including subspaces, linear combinations,
and span, not including bases and dimension).
Relevant Practice Homeworks: 2-5.
Time: 10:30. Duration: 2 hours.
Location: Building 90
/ Rooms 222,223,224,225,226,242,243,244;
Building 92 / Rooms 001,002.
A simple calculator is allowed at the test, no other aids (khomer ezer) are allowed.
Questionnaire
Solutions to Problems 1 and 2
Multiple choice problems:
Problem 3:
the correct answer is item gimmel since we are looking for the span of 2=3-1
(3 variables, rank 1) vectors.
Problem 4:
the correct answer is item gimmel since it really says a=b, so this is is simply the span of the vector (1,1) in C^2.
The second midterm test will take place on Friday, 09.01.2015 (NOTICE THE NEW DATE!).
Material to be covered: vector spaces (bases and dimension), linear transformations;
the material of the first midterm test is not specifically targeted, but it may appear as well.
Relevant Practice Homeworks: 6-8.
Time: 09:00. Duration: 2 hours.
Location: Building 90 / Rooms 222,223,224,225,226,227,243,244;
Building 92 / Rooms 001,002.
A simple calculator is allowed at the test, no other aids (khomer ezer) are allowed.
Questionnaire
Solutions:
Problem 1,
Problem 2-4.
The final exam will be structured as follows:
Duration: 3.5 hours (3 hours and 30 minutes).
Open problems:
you will have to choose 3 open problems out of 4; each open problem is 27 credit points.
Multiple choice problems:
3 multiple choice problems, each one with 4 possible answers;
each multiple choice problem is 7 credit points.
A simple calculator is allowed at the exam, no other aids (khomer ezer) are allowed.
Questionnaire
Solutions: Problem 1
(
page 1,
page 2,
page 3),
Problem 2,
Problem 3,
Problem 4
(
page 1,
page 2).
A useful link with review of some background material.
A course website of Dr. Ahuva Shkop containing many exercises with solutions.
Some algorithms in linear algebra, courtesy of Dr. Ruvim Lipyanski: row reduction of a matrix, solution of a system of linear equations.