Linear Algebra with Computer Science Applications (CSCI 2820)

General information:

Course Description:

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 studnets will become comfortable working with the basic tools in linear algebra and also familiar with several computer science applications throughout the semester.


  • Requires prerequisite courses of (CSCI 2270 or CSCI 2275) and APPM 1360 or MATH 2300 (all minimum grade C-).

List of principal topics includes:

  • Vectors:

    • Notation and terminology

    • Vector operations

    • Inner product

    • Linear functions, Taylor approximation, and regression model

    • Complex numbers and vectors

    • Norm, distance, and angle

    • Linear independence, basis, orthonormal vectors, and Gram–Schmidt algorithm

  • Matrices:

    • Notation and terminology

    • Matrix operations

    • Matrix inverses

    • Orthogonal matrices

    • QR factorization

    • Linear equations

  • Least squares:

    • Least squares data fitting

    • Multi-objective least squares

    • Constrained least squares

    • Nonlinear least squares

  • Eigenvalues and eigenvectors (if we have time)

Lecture Notes:

  • Tentative lecture notes for this course prepared by Prof. S. Boyd and L. Vandenberghe can be found in this link.



  • Assignments: 60%

    • Assignments will be assigned every Wednesday, and due the next week Friday. Please upload an acceptable format, such as jpg or pdf on Canvas (You may take a picture of written howework and upload it).

    • Late policy: Assignment grades will be discounted by 10% every day that the homework is late. After Sunday midnight, late homework will not be accepted.

    • The lowest assignment grade will be dropped.

    • Assignment solutions: Solutions will be posted on Canvas the Monday after they are due.

    • Collaborations are allowed. However, students should come up with their own solutions.

  • Midterm exam (take-home): 25%

  • Final exam (take-home): 25%


Date Topic Lecture Slides Lecture Videos Textbook Chapters
Jan 15 Vectors slide-1 video-1 1.1
Jan 20 Vector addition slide-2 video-2 1.2
Jan 22 Scalar-vector multiplication, Inner product slide-3 video-3 1.3, 1.4
Jan 25 Complexity of vector computations, Linear functions slide-4 video-4 1.5, 2.1
Jan 27 Affine functions, Taylor approximation slide-5 video-5 2.2
Jan 29 Regression model, Norm slide-6 video-6 2.3, 3.1
Feb 1 Distance, Standard deviation slide-7 video-7 3.2, 3.3
Feb 3 Angle, Complexity slide-8 video-8 3.4, 3.5
Feb 5 Clustering, the k-means algorithm slide-9 video-9 4.1, 4.2, 4.3
Feb 8 Examples and applications of clustering slide-10 video-10 4.4, 4.5
Feb 10 Linear dependence, Basis slide-11 video-11 5.1, 5.2
Feb 12 Basis, Orthonormal vectors slide-12 video-12 5.2, 5.3
Feb 15 Gram-Schmidt algorithm slide-13 video-13 5.4
Feb 19 Gram-Schmidt algorithm slide-14 video-14 5.4
Feb 22 Matrices, Zero and identity matrices slide-15 video-15 6.1, 6.2
Feb 24 Matrix addition, norm, Matrix-vector multiplication slide-16 video-16 6.3, 6.4
Feb 26 Complexity, Geometric transformations, Incidence matrix slide-17 video-17 6.5, 7.1, 7.2, 7.3
Mar 1 Convolution slide-18 video-18 7.4
Mar 3 Convolution, Linear and affine functions slide-19 video-19 7.4, 8.1
Mar 5 Affine functions, Linear function models slide-20 video-20 8.1, 8.2
Mar 8 Systems of linear equations slide-21 video-21 8.3
Mar 10 Null space and range space of linear maps slide-22 video-22 Additional note
Mar 12 One-to-one and onto maps, rank of matrices slide-23 video-23 Additional note
Mar 17 Matrix determinant slide-24 video-24 Additional note
Mar 19 Matrix determinant and inverse slide-25 video-25 Additional note
Mar 22 Eigenvalues and eigenvectors of matrices slide-26 video-26 Additional note
Mar 24 Linear dynamical systems slide-27 video-27 9.1, 9.2, 9.3
Mar 29 Matrix-matrix multiplication, Composition of linear functions slide-28 video-28 10.1, 10.2
Mar 31 Matrix power, QR factorization, Left inverses slide-29 video-29 10.3, 10.4, 11.1
Apr 2 Right inverse, Inverse slide-30 video-30 11.1, 11.2
Apr 5 Solving linear equations, Pseudo-inverse slide-31 video-31 11.3, 11.5
Apr 7 Least squares problem, Solution, Solving least squares problems slide-32 video-32 12.1, 12.2, 12.3, 12.4
Apr 9 Least squares data fitting slide-33 video-33 13.1
Apr 12 Least squares data fitting slide-34 video-34 13.1
Apr 14 Validation slide-35 video-35 13.2
Apr 16 Feature engineering, Classification slide-36 video-36 13.3, 14.1
Apr 19 Classification, Least squares classifier slide-37 video-37 14.1, 14.2
Apr 23 Multi-class classifier slide-38 video-38 14.3
Apr 26 Similar matrices, Hermitian matrices slide-39 video-39 Additional note
Apr 28 Hermitian and real symmetric matrices slide-40 video-40 Additional note

Syllabus Statements:

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  • Requirements for COVID-19
    As a matter of public health and safety due to the pandemic, all members of the CU Boulder community and all visitors to campus must follow university, department and building requirements, and public health orders in place to reduce the risk of spreading infectious disease. Required safety measures at CU Boulder relevant to the classroom setting include:

    • maintain 6-foot distancing when possible,

    • wear a face covering in public indoor spaces and outdoors while on campus consistent with state and county health orders,

    • clean local work area,

    • practice hand hygiene,

    • follow public health orders, and

    • if sick and you live off campus, do not come onto campus (unless instructed by a CU Healthcare professional), or if you live on-campus, please alert CU Boulder Medical Services.

      Students who fail to adhere to these requirements will be asked to leave class, and students who do not leave class when asked or who refuse to comply with these requirements will be referred to Student Conduct and Conflict Resolution. For more information, see the policies on COVID-19 Health and Safety and classroom behavior and the Student Code of Conduct. If you require accommodation because a disability prevents you from fulfilling these safety measures, please see the “Accommodation for Disabilities” statement on this syllabus.

      Before returning to campus, all students must complete the COVID-19 Student Health and Expectations Course. Before coming on to campus each day, all students are required to complete a Daily Health Form. In this class, you may be reminded of the responsibility to complete the Daily Health Form and given time during class to complete it. Students who have tested positive for COVID-19, have symptoms of COVID-19, or have had close contact with someone who has tested positive for or had symptoms of COVID-19 must stay home and complete the Health Questionnaire and Illness Reporting Form remotely. In this class, if you are sick or quarantined, please email the instructor about absence due to illness or quarantine.

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  • Religious Holidays
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    See the campus policy regarding religious observances for full details.