# Math 330

# Linear Algebra

## Math 330 (Section 1001), Spring 2024

Lectures: MW 2:30am-3:45 pm in HOS 380

Discussions:

Section 1002: Friday 1:00-2:15pm in CBC C115

Section 1003: Friday 2:30-3:45pm in CBC C115

Instructor: Daniel Corey, daniel.corey[at]unlv.edu

Dan's Office Hours: Monday & Wednesday: 9:30am-11:00am (my office is CDC-09 912)

Graduate Assistant: Linjie Ying, yingl1[at]unlv.nevada.edu

Linjie's office hours: Friday: 11:15am-12:45pm, 3:45pm-5:15pm (Linjie's office is CDC 702)

Textbook: Introuction to Linear Algebra, 6th edition, by Gilbert Strang. Chapters 1-6.

### Key dates

Exam 1: February 23 (Chapters 1-2)

Exam 2: April 5 (Chapters 3-4, except 4.3, 4.5)

Final: May 8 3:10-5:10pm HOS 380 (Comprehensive)

## Lecture Notes

Weekly lecture notes will be posted here.

## Homework

Weekly assignments will be posted here. The underlined part refers to the section in the text, and the numbers refer to the exercises at the end of the respective section.

Assignment 1 1.1: 5, 6, 7, 14, 17 Due Jan 26.

Assignment 2 1.2: 1, 4, 7, 13, 25; 1.3: 4, 6, 7, 8, 14 Due Feb 2

Assignment 3 1.4: 3, 6, 7, 14; 2.1: 3, 6, 11, 12, 18, 20 Due Feb 9

Assignment 4 2.2: 4, 15, 16, 19, 28, 32; 2.3: 3, 5, 7, 10 Due Feb 16

Assignment 5 2.4: 8, 9, 14, 18, 19, 30, 3.1: 9, 11, 12, 24 Do not turn in.

Assignment 6 3.2: 4, 6, 13, 17, 35, 3.3: 4, 6, 20, 28, 31 Due March 8

Assignment 7 3.4: 2, 10, 14, 16, 41; 3.5: 3, 11, 12, 14, 32 Due March 22

Assignment 8 4.1: 3, 13, 14, 17, 22 4.2: 0, 1, 3, 5 Due March 29

Assignment 9 4.2: 12, 13, 20, 22, 23; 4.4: 1, 2, 5, 11, 18 Do not turn in.

Assignment 10 5.1: 3, 4, 5, 6, 7, 8, 9, 13, 14, 17 Due April 12.

Assignment 11 5.2: 2, 6, 12, 15, 16, 17; 5.3: 3, 4, 7, 11 Due April 19.

Assignment 12 6.1: 2, 3, 4, 6, 15, 16, 17, 18, 27, 29 Due April 26.

Assignment 13 6.2: 2, 7, 11, 25, 29, 30 6.3 2, 6, 11, 14a-d Do not turn in.

## Schedule

Below is the plan for the semester. I will update this regularly. Take this as a rough guide; if a topic is not explicitly mentioned here, this does not mean it is or is not covered.

### Week 1: Overview, 1.1

Dates: Jan 17 - Jan 19

Topics: Overview; vectors and linear combinations

### Week 2: 1.2-1.4

Dates: Jan 22 - Jan 26

Topics: dot product, length, and angle; matrices and their column spaces; linear (in)dependence; row/column rank; row and column picture of matrix multiplication; properties of matrix multiplication.

### Week 3: 1.4 - 2.1

Dates: Jan 29 - Feb 2

Topics: ; A=CR factorization; Solving Ax=b where A is square; elimination and back substitution.

### Week 4: 2.2-2.3

Dates: Feb 5 - Feb 9

Topics: Inverse matrices and their properties; Elimination matrices and their inverses; LU-factorization.

### Week 5: 2.4 - 3.2

Dates: Feb 12 - Feb 16

Topics: Permutation matrices; permuting rows and columns; elimination with row exchanges PA=LU; transpose; symmetric matrices; vector spaces Rn ; fundamental subspaces: row space, column space, left/right null space, Solving Rx=0 where R is in row-reduced echelon form.

Skipped: Section 2.5 Derivatives and finite difference matrices.

### Week 6: Review, Exam 1

Dates: Feb 21 - Feb 23 (No lecture Feb 19 for Presidents day)

Topics: Review; Exam 1 on Friday Feb 23.

### Week 7: 3.2 - 3.4

Dates: Feb 26 - Mar 1.

Topics: Row-reduced echelon form, computing the nullspace N(A), A = CR revisited, the complete solution to Ax=b, linear independence.

### Week 8: 3.4-3.5

Dates: Mar 4 - Mar 8

Topics: Spanning, bases, and dimension.

Skipped: Graphs, rank 2 matrices.

### Week 9: 4.1-4.2

Dates: Mar 18 - Mar 22 (No class Mar 11-15 for spring break)

Topics: Orthogonality of vectors and subspaces, orthogonal complement, projection onto a line

### Week 10: 4.2, 4.4

Dates: Mar 25 - Mar 29

Topics: Orthogonal projection onto a subspace, orthonormal bases, orthogonal matrices, Gram-Schmidt.

Skipped: Least squares approximation (4.3) and the pseudoinverse of a matrix (4.5).

### Week 11: 5.1, Review, Exam 2

Dates: Apr 1 - Apr 5

Topics: Determinants, Review

Note: Exam 2 on Friday April 5

### Week 12: 5.2-5.3

Dates: Apr 8 - Apr 12

Topics: Big formula, axioms for determinants, properties for determinants, pivot formula, Cramer's rule, determinants and volume, A=QR decomposition.

### Week 13: 6.1

Dates: Apr 15 - 19

Topics: Definitions of eigenvalues and eigenvectors, geometric examples (projection, reflection, rotation), equation for eigenvalues, eigenvalue problem, complex eigenvalues, algebraic / geometric multiplicity

Skipped: Markov matrices

### Week 14: 16.2-16.3

Dates: Apr 22 - Apr 26

Topics: Diagonalizing a matrix, eigenvectors of different eigenvalues are linearly independent, determinant and trace, similar matrices, Fibonacci numbers, spectral theorem.

Skipped: Positive definite matrices, optimization and machine learning.

### Week 15: Study week

Review.