MATH321-001 32505 Linear Algebra

Time TTh 1400-1515, Location DSH-228


Instructor: Dimiter Vassilev     Office :  SMLC, Office 326  Email:  Phone Number: 505 277 2136


Office Hours: Tuesday 9:30-10:30 & Thursday 4:30-5:30pm. Feel free to stop-by anytime when you have a quick question.


Homework: Quick link to the Homework.

Textbook: Linear Algebra done wrong, S. Treil. We will cover most of Chapters 1-6 and parts of Chapters 7-9.

Other texts:

Catalog Description: Linear transformations, matrices, eigenvalues and eigenvectors, inner product spaces. Prerequisite: C in 264.

Please note the following guidelines for the course:

GRADING: Your total course grade is based on your ranking and percentile in the class computed using the in-class exams, homework, and the final exam scaled as follows:

The Final Exam score will replace all midterm scores that are lower than the Final Exam score. All grades will be posted on UNMLearn. Although a small curve might be used, 90% , 80% or 70% of the possible maximum points guarantees at least an A, B or C, respectively.

To get full credit on exams, homework and quizzes you need to show your work, neatly, in clear and correct mathematical notation, annotated by English sentences where appropriate. You will be graded based on the work shown, not on the answer. All grades will be posted on UNMLearn. If you withdraw after the 3rd week of class, you will receive a W. If you do not withdraw, you will receive a letter grade of A,B,C,D or F (and not a W).

CALCULATORS: We will not use any (graphing or non-graphing) calculators on the exams or quizzes.

EXAMS: The exam dates are given in the syllabus. No makeup exams will be given unless you contact your instructor ahead of time with a documented “university authorized absence” (illness, family emergency, active participation in scholarly or athletic events).

ATTENDANCE: Attendance at UNM and homework is mandatory. If you have missed more than 4 attendance+homework+quizzes in the first 3 weeks you will be dropped from the course. Similarly, students with absences and lack of work during the rest of the semester may be dropped. Tardiness or early departure may be regarded as absence. Please note that it is the students responsibility to drop the course if he/she stops attending. A failing grade of F may be assigned if the student stops attending and does not drop. You can find the precise statemenet of the University policy here.

Be courteous and respectful and refrain from any activity that could be disruptive to the class. Cheating will not be tolerated.

ACCESSIBILITY STATEMENT: In accordance with University Policy 2310 and the Americans with Disabilities Act (ADA), academic accommodations may be made for any student who notifies the instructor of the need for an accommodation. It is imperative that you take the initiative to bring such needs to the instructor’s attention, as he/she are not legally permitted to inquire. Students who may require assistance in emergency evacuations should contact the instructor as to the most appropriate procedures to follow. Contact Accessibility Resource Center at 277-3506 for additional information

FINAL EXAM: Tuesday, May 7, 10:00 a.m.‐12:00 p.m. Students having conflicts with this exam schedule must notify the
appropriate instructor before Friday, March 29, 2019. Any student having more than three examinations scheduled in any one day may notify the instructor of the last examination listed. If notified before Friday, March 29, 2019, the instructor shall make arrangements to give a special examination. Changes in this examination schedule are not permitted except by formal approval of the instructor’s College Dean.

HOMEWORK: Homework related material including solutions of some problems will be posted on UNMLearn. The general rule is that homework assigned in one week is due at the beginning of the Tuesday or the first class of the following week. No late homework will be accepted. You have to turn in the solutions of the homeowork problems in the same order and number as they appear on the pdf version of the assignment posted on UNMLearn. Not all homework problems will be graded. You will get a credit of 4 points on each homework assignment as long as you turn in the wording of all problems written in the correct order. The remaining 16 points will be awarded based on your solutions of selected 4-6 problems.

Class Week


Topics and Section


Homework (dthe 1st class of

the following week)

1. Jan 14

1.1-1.2 Vector spaces - linear combinations, bases.


2. Jan 21

1.2 More on bases; 1.3 - 1.5 Linear transformations - matrix representations using bases,

composition of linear transformations and multiplication of matrices.


3. Jan 28

vector space structure, trace of a matrix. Complex vector spaces, real vs. complex linear maps in the plane.


4. Feb 4

1.6 Linear isomorphisms/ invertible maps. Dimension of a finite dimensional vector space.


5. Feb 11

1.7 Linear subspaces - rank and nullity of a linear map. The rank-nullity theorem. Sums and direct sums

of sub-spaces. Dimension of a sum of subspaces.


6. Feb 18

Feb. 19: snow day. Product of vector spaces. Quotient spaces.


7. Feb 25

Exam 1 on Tuesday Feb. 26. Solutions for Exam 1. Basis and dimension of quotient spaces.

8. March 4

2.2 Echelon and reduced echelon forms. Solving a linear system.

2.3 & 2.7 (finding) basis and dimension of the null space.

HW7 (due March 19)

9. March 11

March 10-17 Spring Break

10. March 18

2.7 Column space = range; (finding) basis and dimension of the column space. Row space and R(A^t).

Finding bases of the four fundamental spaces.


11. March 25 LU decomposition; 2.4 computing A^{-1}. 2.8 Change of coordinates.HW9:

12. Apr 1

Dual vector space-dimension and basis, space of multilinear functions,

skew-symmetric and symmetric forms; space of top (skew-symmetric) forms; permutations; the determinant.


13. Apr 8


Computing the determinant of a matrix using row/column operations. Co-factor expansion,

computing the inverse using the adjugate (Cramer's rule)


14. Apr 15

Eigenvectors and eigenvalues of a linear operator. Characteristic polynomial. Diagonalizable operators.

Inner product (real and complex) vector spaces - norm, the Cauchy-Schwarz inequality, orthogonality, orthonormal

set, coordinates in an orthonormal basis.

Exam 2 on Thursday April 18.


15. Apr 22

The Gram-Schmidt orthogonalization. Orthogonal projections - orthogonal complement, distance

minimizing properties, Bessel's inequality. The Riesz representation theorem.


16. Apr 29

Adjoint operator. Self-adjoint operators, the spectral theorem for self-adjoint operators on a real

inner product space. Self-adjoint operaors on complex and real inner product spaces - orthogonality

of the ditinct eigenspaces and properties of the spectrum.

No homework.

Tuesday May 7

Final Exam 10:00 a.m.‐12:00 p.m. in the usual room, double check with the Official Schedule