**330 LINEAR ALGEBRA I (3+0) 3 credits**

Vector analysis continued; abstract vector spaces; bases, inner products; projections; orthogonal complements, least squares; linear maps, structure theorems; elementary spectral theory; applications. Corequisite(s): MATH 283 R.

Instructor Course Section Time ------------------------------------------------------------------------ Eric Olson Math 330-1006 Linear Algebra 11:00-11:50AM MWF PE103

- Instructor:
- Eric Olson
- email:
- Please contact me through WebCampus
- Office:
- MWF 1:00-1:50PM in DMS 238 and through Zoom by appointment
- Homepage:
- http://fractal.math.unr.edu/~ejolson/330/
- Live Stream:
- If you can't come to class due to sickness, quarantine or other reasons, please join via the Zoom link in WebCampus.
- Grader:
- to be determined (contact through
WebCampus)
- Required Texts:
- Linear Algebra and Its Applications, n-th Edition by David C. Lay.
- https://www.pearson.com/mylab
(class registration code)
- Other resources:
- MIT Open Courseware, Gilbert Strang, Spring 2010.
- 18-06-linear-algebra-spring-2010
- Introduction to Applied Linear Algebra, Boyd and Vandenberghe.
- http://vmls-book.stanford.edu/

- Solve linear systems using Gaussian elimination.
- Minimize least squares by Gram-Schmidt orthogonalization.
- Find LU, QR and UΣV
^{T}matrix factorizations.

- Lecture 1: Overview of the Course
- Lecture 2: Systems of Linear Equations
- Lecture 3: Unique Solutions
- Labor Day: no notes
- Lecture 4: Echelon Form
- Lecture 5: Solving Systems
- Lecture 6: Matrix-Vector Products
- Lecture 7: Linear Dependence
- Lecture 8: Linear Transformations
- Lecture 9: Fish and Sheep
- Lecture 10: Matrix-Matrix Products
- Lecture 11: Inverse Matrices
- Lecture 12: Matrix Transpose
- Lecture 13: Matrix of a Row Operation
- Lecture 14: LU Factorization
- Lecture 15: Col(A) and Nul(A)
- Lecture 16: More Subspace Examples
- Exam 1: no notes
- Lecture 17: Introduction to Determinants
- Lecture 18: Determinants and Row Operations
- Lecture 19: Determinants and Invertibility
- Lecture 20: Cramer's Rule
- Lecture 21: Formula for the Inverse
- Lecture 22: Subspaces Again
- Lecture 23: More Subspaces
- Lecture 24: Even More Subspaces
- Nevada Day: no notes
- Lecture 25: The Basis Theorem
- Lecture 26: Change of Basis
- Lecture 27: Eigenvalues and Eigenvectors
- Lecture 28: Characteristic Polynomial
- Lecture 29: Diagonalization
- Veteran's Day: no notes
- Lecture 30: Basis of a Linear Transformation
- Lecture 31: Complex Numbers
- Exam 2: no notes
- Lecture 32: Complex Eigenvalues
- Lecture 33: Orthogonality
- Thanksgiving: no notes
- Lecture 34: Orthogonal Projections
- Lecture 35: Gram-Schmidt
- Lecture 36: QR and Least Squares
- Lecture 37: QR Factorization Example
- Lecture 38: The Spectral Theorem
- Lecture 39: Singular Value Decomposition
- Review: Final Exam Review

- Written Homework 1
- Written Homework 2
- Written Homework 3
- Written Homework 4
- Written Homework 5
- Written Homework 6
- Written Homework 7

- Section 6.1 # 35

- Section 6.4 # 23

- Section 6.4 # 24

- Section 5.1 # 31

- Section 5.2 # 20

- Section 5.3 # 33

- Section 4.1 # 40

- Section 4.2 # 47

- Section 4.2 # 48

- Section 3.2 # 37

- Section 3.2 # 41

- Section 3.2 # 49

- Section 2.3 # 36

- Section 2.8 # 43

- Section 2.9 # 28

- Section 2.1 # 28

- Section 2.2 # 23

- Section 2.2 # 31

- Section 1.4 # 14

- Section 1.4 # 44

- Section 1.4 # 46

My lecture notes should complement the notes you take in class. I'd recommend comparing the notes you take with the ones I post after class along with the relevant sections from the text. Then use these three sources of information to create a final version of your notes. In my experience reviewing the lecture in this way is important. Though tempting with an iPad, one should not try make the final version of your lecture notes during class. That takes too much time and omits the comparison and review steps mentioned above.

We will be using WebCampus to turn in written homework--either scanned from pencil and paper or prepared digitally using an iPad or similar device. In addition there will be online exercises available from the Pearson MyLab webpage. In addition to the exercises and written homework, there will be two exams and a final exam. In person attendance is mandatory for all exams and the final.

Exam 1 50 points Exam 2 50 points MyLab Math Online 50 points Handwritten Homework 50 points Final 100 points ------------------------------------------ 300 points totalExams and quizzes will be interpreted according to the following grading scale:

Grade Minimum Percentage A 90 % B 80 % C 70 % D 60 %The instructor reserves the right to give plus or minus grades and higher grades than shown on the scale if it is believed they are warranted.

Aug 28 -- Overview of the Text Aug 30 -- Section 1.1 Systems of Linear Equations Sep 01 -- Section 1.2 Row Reduction and Echelon Forms Sep 04 ***Labor Day*** Sep 06 -- Section 1.4 The Matrix Equations Ax=b Sep 08 -- Section 1.5 Solution Sets of Linear Systems Sep 11 -- Section 1.5 Solution Sets of Linear Systems (continued) Sep 13 -- Section 1.7 Linear Independence Sep 15 -- Section 1.8 Introduction to Linear Transforms Section 1.9 The Matrix of a Linear Transformation Sep 18 -- Section 2.1 Matrix Operations Sep 20 -- Section 2.2 The Inverse of a Matrix Sep 21 -- Section 2.3 Characterizations of Invertible Matrices Sep 25 -- Section 2.4 Partitioned Matrices Sep 27 -- Section 2.5 Matrix Factorizations Sep 29 -- Section 2.5 Matrix Factorizations (continued) Oct 02 -- Section 2.8 Subspaces of R^{n}Oct 04 -- Section 2.9 Dimension and Rank Oct 06 -- Exam 1 Oct 09 -- Section 3.1 Introduction to Determinants Oct 11 -- Section 3.2 Properties of Determinants Oct 13 -- Section 3.3 Cramer's Rule, Volume and Linear Transformations Oct 16 -- Section 3.3 Cramer's Rule, Volume and Linear Transformations (continued) Oct 18 -- Section 4.1 Vector Spaces and Subspaces Oct 20 -- Section 4.2 Null Spaces, Column Spaces, Row Spaces and Linear Transformations Oct 23 -- Section 4.2 Null Spaces, Column Spaces, Row Spaces and Linear Transformations (continued) Oct 25 -- Section 4.3 Linearly Independent Sets; Bases Oct 27 ***Nevada Day*** Oct 30 -- Section 4.5 The Dimension of a Subspace Nov 01 -- Section 4.6 Change of Basis Nov 03 -- Section 5.1 Eigenvalues and Eigenvectors Nov 06 -- Section 5.2 The Characteristic Equations Nov 08 -- Section 5.3 Diagonalization Nov 10 ***Veteran's Day*** Nov 13 -- Section 5.4 Eigenvectors and Linear Transformations Nov 15 -- Section 5.5 Complex Eigenvalues Nov 17 -- Exam 2 Nov 20 -- Section 6.1 Inner Product, Length and Orthogonality Nov 22 -- Section 6.2 Orthogonal Sets Nov 24 ***Family Day*** Nov 27 -- Section 6.3 Orthogonal Projections Nov 29 -- Section 6.4 The Gram-Schmidt Process Dec 01 -- Section 6.5 Least Squares Problems Dec 04 -- Section 7.1 Diagonalization of Symmetric Matrices Dec 06 -- Section 7.4 The Singular Value Decomposition Dec 08 -- Section 7.4 The Singular Value Decomposition (continued) Dec 11 -- Review Dec 13 ***Prep Day*** Dec 20 Final Exam from 10:15am-12:15pm

During the epidemic I discovered that Zoom also allowed me to meet individually with students who are sick or can't come to campus just to ask a question. If you wish to set up an appointment for office hours please send me a message through WebCampus.

Exams and quizzes, unless otherwise noted, will be closed book, closed notes and must reflect your own independent work.

If you are unclear as to what constitutes cheating, please consult with me.

Last Updated: Sat Aug 26 10:48:12 AM PDT 2023