1.2.7. Week 7 - 10/6

Agenda for this week:

This week we cover how to solve square matrix systems of linear equations.

Reading:

• 6.3. Geometric Transforms – skip

• 6.4. Systems of Linear Equations

• 6.5. Elimination

• 6.6. LU Decomposition

• 6.7. Cholesky Decomposition for Positive Definite Systems

• 6.8. (optional) Linear System Applications

• 6.9. Numerical Stability

2025 Video Lectures:

• Section 6.4 - Systems of Linear Equations

• Section 6.4.4 - The Column - Row Factorization

• Section 6.4.5 - The Column and Row View

• Section 6.5 - Elimination - part 1

• Section 6.5 - Elimination - part 2

• I made a mistake and LU Decomposition wasn’t recorded, so see the recording from last year.

• Section 6.6 - LU Decomposition - 2024

• Section 6.7 - Cholesky Decomposition

• Section 6.9 - Numerical Stability

2024 Video Lectures:

• Section 6.4 - Systems of Linear Equations - 2024 (15:00)

• Section 6.4.5 - The Row and Column View - 2024 (9:19)

• Section 6.5 - Elimination - 2024 (17:38)

• Section 6.5.3 - Elimination to find the Matrix Inverse - 2024 (8:14)

• Section 6.7 - Cholesky Decomposition - 2024 (11:01)

• Optional Section 6.8 - Linear Systems Applications (21:10)

Annotated notes:

• Section 6.1 - Introduction to linear algebra and vectors notes/S6_1_vectors.pdf

• Section 6.2 - Working with Matrices notes/S6_2_matrices.pdf

• Wall fallowing vectors - notes/Wall-fallow-vectors.pdf

• Matrices from in class - notes/Matrices.pdf

• Determinant - notes/Determinant.pdf

• Change of Coordinate Frame - notes/Change-coord.pdf

• Systems of Equations - notes/S6_4_Systems_Eq.pdf

• Elimination - notes/Elimination.pdf

• Column View of Systems of Equations - notes/Column-View.pdf

• LU Decomposition - notes/LU-Decomposition.pdf

• LU Decomposition Update - notes/LUdecomp.pdf

• Cholesky Decomposition Example - notes/Cholesky_example.pdf

Assignments:

• Skip - A Change of Coordinate Frames

• Matrix Homework, Hints for Matrix Homework Assignment

• Attendance Quizzes: AQ06_1, AQ06_2, AQ06_4, Week 7 Attendance Quiz Hints