Matrices and Matrix Calculations (M340L)

Course information:

Unique: 54165

Lecture: 3:30-5:00pm, T Th, CPE 2.214

There is no required text for this course. Learning modules covering each lecture can be found on Quest at https://quest.cns.utexas.edu/

Recommended course texts:

1. Linear Algebra and Its Applications, by David C. Lay.

2. Signals and Systems, edited by Richard Baranuik. Click for PDF

3. Linear algebra, signal processing, and wavelets. A unified approach. Python version. By Oyvind Ryan. Click for PDF

Instructor: Arie Israel (arie AT math DOT utexas DOT edu)

Office hours: 9:00am-12:00pm, W, RLM 12.126

TA: Carter Smith (cartersmith AT utexas DOT edu)

TA office hours: 9:30-11:30am, T Th, RLM 11.104

First day handout:

Schedule:

• Lecture 1 (08/30)
• Lecture 2 (09/04)
• Lecture 3 (09/06)
• Lecture 4 (09/11)
• Lecture 5 (09/13)
• Lecture 6 (09/18)
• Lecture 7 (09/20)
• Lecture 8 (09/25):
• Lecture 9 (09/27)
• Midterm Exam 1 (10/02)
• Lecture 10 (10/04)
• Lecture 11 (10/09)
• Lecture 12 (10/11)
• Lecture 13 (10/16)
• Lecture 14 (10/18)
• Lecture 15 (10/23)
• Lecture 16 (10/25)
• Lecture 17 (10/30)
• Lecture 18 (11/01)
• Midterm Exam 2 (11/06)
• Lecture 19 (11/08)
• Lecture 20 (11/13)
• Lecture 21 (11/15)
• Lecture 22 (11/20)
• Lecture 23 (11/27)
• Lecture 24 (11/29)
• Midterm Exam 3 (12/04)
• Final Review (12/06): Review
• Final Exam (12/18): 9-12 PM; Location: CPE 2.214

Lecture 1: Matrix Algebra, Reduced Row Echelon Form

Learning Modules:

• LM 00a (Vectors and Matrices), LM 00c (Reduced Row Echelon Form), LM 01a (Matrix Algebra)

Notes:

• lecture 1

Lecture 2: Linear Systems

Learning Modules:

• LM 00b (Linear Systems: Gauss Elimination), LM 01b (Linear Systems)

Notes:

• lecture 2

Lecture 3: Linear Systems, Invertibility

Learning Modules:

• LM 00d (Matrix Inverses), LM 00e (Determinants)

Notes:

• lecture 3

Lecture 4: Invertibility

Learning Modules:

• LM 00d

Notes:

• lecture 4

Just for fun:

• Blue-Eyed Islanders Puzzle

Lecture 5: Vector Spaces

Learning Modules:

• LM 002

Notes:

• lecture 5

Lecture 6: Subspaces and Span

Learning Modules:

• LM 003

Notes:

• lecture 6

Lecture 7: Linear Independence and Bases

Learning Modules:

• LM 004

Notes:

• lecture 7

Lecture 8: Fundamental Matrix Subspaces

Learning Modules:

• LM004, LM 005

Notes:

• lecture 8

Lecture 9: Fundamental Matrix Subspaces

Learning Modules:

• LM 005

Notes:

• lecture 9
• review sheet

Lecture 10: Linear Transformations

Learning Modules:

• LM 006

Lecture 11: Linear Transformations

Learning Modules:

• LM 006

Lecture 12: Complex Signals

Learning Modules:

• LM 007

Notes:

• lecture 12

Lecture 13: Inner Product Spaces and Orthogonality

Learning Modules:

• LM 008

Notes:

• lecture 13

Lecture 15: Fourier Series II

Learning Modules:

• LM 009

Notes:

• lecture 15

Lecture 16: Orthogonal Projections and Gram-Schmidt

Learning Modules:

• LM 10a,10b

Notes:

• lecture 16

Lecture 17: Gram-Schmidt and QR Decompositions

Learning Modules:

• LM 10b

Notes:

• lecture 17

Lecture 18: Discrete Orthonormal Bases

Learning Modules:

• LM 11

Notes:

• lecture 18

Lecture 19: Discrete Fourier Analysis

Learning Modules:

• LM 12

Notes:

• lecture 19

Lecture 20: Eigenvectors and Eigenvalues

Learning Modules:

• LM 13

Notes:

• lecture 20

Lecture 21: Diagonalization

Learning Modules:

• LM 14

Notes:

• lecture 21

Lecture 22: Markov Chains

Learning Modules:

• LM 15

Notes:

• lecture 22

Lecture 23: Differential Equations

Learning Modules:

• LM 16

Notes:

• lecture 23

Lecture 24: LTI Systems

Learning Modules:

• LM 17, partial coverage of LM 18
• LM 19 (optional additional reading on convolutions)

Notes:

• lecture 24