Subject 
In brief, this course introduces the fundamentals of linear algebra in the context of computer science applications. It includes definitions of vectors and matrices, their various operations, linear functions and equations, and least squares. It also includes the basics of floating point computation and numerical linear algebra. The list of covered topics are mentioned in details below. In this course, the students will become comfortable working with the basic tools in linear algebra and also familiar with several computer science applications throughout the semester. . 
Prerequisites 
Mathematical maturity; Requires prerequisite courses of (CSCI 2270 or CSCI 2275) and APPM 1360 or MATH 2300 (all minimum grade C). If you have not taken those classes but believe that your background is close to being sufficient, please make sure you have filled up any potential gaps by the end of the second week of classes. If you are not sure whether your background suffices, please see the instructor. 
Instructor 
Alexandra Kolla (alexandra.kolla [at] colorado [dot] edu) 122 ECES [AK] 
Canvas 

Course Staff 
GSS: Nivetha Kesavan (Nivetha.Kesavan@colorado.edu), Rick Gentry (Rick.Gentry@colorado.edu). CA: Zackary Jorquera (Zackary.Jorquera@colorado.edu)

Times 
TTh 02:20 PM  03:35 PM 
Class location (Zoom Link) 
https://cuboulder.zoom.us/j/7640842775 
Office Hours 
Alexandra Kolla: Tuesdays 1:202:20 pm at this zoom link. Nivetha Kesavan: M W F 3:30 pm 4:30 pm at this zoom link, and Passcode: 345353. Rick Gentry: Tuesdays 45 pm, Thursdays 11am12 noon at this zoom link. Zackary Jorquera: M 1:004:00 pm, Th: 3:306:00 pm, F 1:004:00 pm at this zoom link. 
#  Date  Topic  Lecture Slides  Lecture Videos  Textbook Chapters 

1  T August 25  Introduction to Vectors  Slides (accidentally deleted the annotated slides, please read book chapters instead)  Video Recording  1.11.3 
2  Th August 27  Linear Combinations of Vectors, Inner Product, Complexity  Slides  Video Recording  1.41.5 
3  Tu September 1  Linear Functions  Slides  Video Recording  2.1 
4  Th September 3  Norm and Distance  Slides  Video Recording  3.1, 3.2 
5  Tu September 8  Distance, Standard Deviation  Slides  Video Recording  3.2, 3.3 
6  Th September 10  Angles, CauchySchwartz, Complexity  Slides  Video Recording  3.4, 3.5 
7  Tu September 15  Linear Independence, Bases  Slides  Video Recording  5.1, 5.2. Also see chapter 2 of this book for vector space material. 
8  Th September 17  More on Vector Spaces, Orthonormal Vectors  Slides  Video Recording  5.3, 5.4 and previous notes on vector spaces above 
9  Tu September 22  More on Vector Spaces, GramSchmidt  Slides  Video Recording  5.4 and previous notes on vector spaces above 
10  Th September 24  GramSchmidt  Slides  Video Recording  5.5 
11  Tu September 29  Review on Vector Spaces, Subspaces, Linear Independence, Basis  Slides  Video Recording  Chapter 4.1 and 4.3 of this book 
12  Th October 1  Review on Basis, Orthogonality, Coordinate systems, Orthogonal Projections  Slides, Slides  Video Recording  Chapters 4.4, 4.5, 6.1 and 6.2 of this book 
13  Tu October 6  Orthogonal Decomposition, Gram Schmidt  Slides  Video Recording  Chapters and 6.26.4 of this book 
14  Th October 8  Review  Video Recording  
15  Tu October 13  Matrices  Slides  Video Recording  Chapters 6.16.3 of textbook 
16  Th October 15  Matrices, continued  Slides  Video Recording (Unfortunately, I only hit "record" mid way through lecture. Luckily, the first 2030 mins are covered extensively in chapter 6.4 of the textbook)  Chapters 6.4 of textbook 
17  Tu October 20  Matrix examples and operations  Slides  Video Recording  Chapters 7.1 of textbook and 2.1,2.2 of this book 
18  Th October 22  Vector Valued Linear Functions, Linear Systems  Slides  Video Recording  Chapter 8 of textbook 
19  Tu October 27  Matrix Multiplication, Paths in Directed Graphs, QR factorization  Slides  Video Recording  Chapter 10 of textbook 
20  Th October 29  Matrix Inverses  Slides  Video Recording  Chapters 11.1,11.2 of textbook 
21  Tu November 3  Matrix Inverses contd. Solving Systems of Linear Equations  Slides  Video Recording  Chapters 11.211.5 of textbook 
22  Th November 5  Row equivalence, echelon form, column space, rank, nullspace  Slides  I did not hit "record" this lecture, I apologize. See math book instead  Chapters 1.11.2 and 2.82.9 of this book 
23  Tu November 10  Determinants  Slides  Video Recording  Chapters 3.13.2 of this book 
24  Th November 12  Determinants, contd.  Slides  Video Recording  Chapters 3.33.4 of this book 
25  Tu November 17  Eigenvectors and Eigenvalues  Slides  Video Recording  Chapters 5.15.2 of this book 
26  Th November 19  Eigenvectors and Eigenvalues, contd.  Slides  Video Recording  Chapters 5.25.3 of this book 
27  Tu November 24  Review session  Slides  Video Recording  
28  Th November 26  No Class, Thanskgiving  
29  Tu December 1  Complex eigenvalues and eigenvectors  Slides  Video Recording  Chapters 5.5 of this book 
30  Th December 3  Review For Final  Video Recording 
Homework #  Due  Homework Solutions 

HW0  TBD  Solutions 
HW1  TBD   
HW2  TBD   
HW3  TBD   
HW4  TBD   
HW5  TBD   
Homework 

There will be weekly homework. 
Students are encouraged to collaborate, but each homework has to be turned in individually by each student . 
There are *ABSOLUTELY NO LATE HOMEWORKS* accepted. Instead, I will be dropping the lowest two homework grades. 
Please do not forget to cite your collaborators and sources (you will get a zero if you use material from elsewhere and do not cite the source!) 
Exams 

There will be two midterms and a Final exam in the "takehome exam" format. More details to come. 
Grading 

60% homeworks, 15% each midterm, and 20% final exam. 

Chapters 15: "Vectors" 
 We will start with "basic" Notation and terminology. Vector operations. Vector Spaces. Inner product. Linear functions, Taylor approximation and regression model. Complex numbers and vectors. Norm, distance, and angle. Linear independence, basis, orthonormal vectors, and Gramâ€“Schmidt algorithm. 
Chapters 611: "Matrices"

 Notation and terminology. Matrix operations. Matrix inverses. Orthogonal matrices. QR factorization, Diagonalization. Linear equations. 
Chapter 1219: "Least Squares"

 Least squares data fitting. Multiobjective least squares. Constrained least squares. Nonlinear least squares. 
Not in the Book: "Eigenvalues and Eigenvectors"

 Matrix Spectra. Eigendecomposition. Eigenvalues and Eigenvectors. 