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Math 4153
Finite Dimensional Vector spaces
TextBook: Abstract Linear Algebra --- Morton L. Curtis
References
Office Hours: MWF 11-12 at 246 Lockett
Grader: Siddiqur Rahman
Office Hours: T, Th: 1- 3 PM at 377 Lockett
If the office hours do not work for you, please send us emails to make an appointment.
References
Office Hours: MWF 11-12 at 246 Lockett
Grader: Siddiqur Rahman
Office Hours: T, Th: 1- 3 PM at 377 Lockett
If the office hours do not work for you, please send us emails to make an appointment.
Homework: 20
Midterm: 60, 20 each: Feb 9, Mar 23, Apr 20
Final: 30, May 3 Thursday, 7:30am-9:30am
Final Problem Set Here is a list of the questions that might be helpful to prepare the Final. Although the questions on Final will not be 100% the same as the questions on the problem set, the concepts are the same and useful.
Midterm: 60, 20 each: Feb 9, Mar 23, Apr 20
Final: 30, May 3 Thursday, 7:30am-9:30am
Final Problem Set Here is a list of the questions that might be helpful to prepare the Final. Although the questions on Final will not be 100% the same as the questions on the problem set, the concepts are the same and useful.
Outline:
In class, I would like to use slides to present/recall important definitions and statements so that we can have more time to look at examples and proofs.
Chapter I: Vector Spaces and Linear Maps
Section A: Vector Spaces
Section B: Linear Transformations
Section C: Bases and Dimension - Part 1 Part 2
Chapter II: Matrices and Determinants
Section A: Matrices
Section C, D: Determinants and Inverses
Section E: Eigenvectors and Eigenvalues (updated, Mar 1)
Section II-E & I-D: Diagonalization and Direct Sums
Chapter IV: Inner Product Spaces
Section A, B, C: This part was covered by Mr. Po-Han Hsu, so please check the slides (provided by Po-Han) on the moodle page.
Section D: Orthogonal and Unitary Matrices
Section E+: Spectral Theorem --- Matrix Version
The Spectral Theorem
Chapter III: Rings and Polynomials
Section C: Cayley-Hamilton Theorem --- Class Slides
In class, I would like to use slides to present/recall important definitions and statements so that we can have more time to look at examples and proofs.
Chapter I: Vector Spaces and Linear Maps
Section A: Vector Spaces
Section B: Linear Transformations
Section C: Bases and Dimension - Part 1 Part 2
Chapter II: Matrices and Determinants
Section A: Matrices
Section C, D: Determinants and Inverses
Section E: Eigenvectors and Eigenvalues (updated, Mar 1)
Section II-E & I-D: Diagonalization and Direct Sums
Chapter IV: Inner Product Spaces
Section A, B, C: This part was covered by Mr. Po-Han Hsu, so please check the slides (provided by Po-Han) on the moodle page.
Section D: Orthogonal and Unitary Matrices
Section E+: Spectral Theorem --- Matrix Version
The Spectral Theorem
Chapter III: Rings and Polynomials
Section C: Cayley-Hamilton Theorem --- Class Slides
Simple Notes --- Spectral Theorems
I will split the section III-C: Spectral Theorems into few parts. In these notes, I summarize some basic properties without proofs. Please find examples on the slides.
Part 1: Diagonalization . 2 easy examples
Part 2: Inner Product Space
I will split the section III-C: Spectral Theorems into few parts. In these notes, I summarize some basic properties without proofs. Please find examples on the slides.
Part 1: Diagonalization . 2 easy examples
Part 2: Inner Product Space
Homework Assignments:
Feb 2: Section I-A: 1, 2, 3, 7(Triangular case), 9
Section I-B : 1, 5, 7
Feb 9: Section I-B : 2, 3, 6
Section I-C : 2
Feb 23: Section I-C : 5, 6, 7, 9 ,10
Mar 2: Section I-C : 4
Section II-A : 2, 8
Section II-C : 1, 2
Mar 9: Section II-C: 3
Section II-D: 1, 3
Section I-E : 1, 3, 5
Mar 16: Section I-E : 6, 7
Section II-E : 1, 2, 3, 4
Mar 21: Section III-A: 6, 7, 8
April 6 : Section I-D: 2, 6, 7
Section IV-A: 2, 3, 4
Feb 2: Section I-A: 1, 2, 3, 7(Triangular case), 9
Section I-B : 1, 5, 7
Feb 9: Section I-B : 2, 3, 6
Section I-C : 2
Feb 23: Section I-C : 5, 6, 7, 9 ,10
Mar 2: Section I-C : 4
Section II-A : 2, 8
Section II-C : 1, 2
Mar 9: Section II-C: 3
Section II-D: 1, 3
Section I-E : 1, 3, 5
Mar 16: Section I-E : 6, 7
Section II-E : 1, 2, 3, 4
Mar 21: Section III-A: 6, 7, 8
April 6 : Section I-D: 2, 6, 7
Section IV-A: 2, 3, 4
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