#### Tue 5/16: Last Applications of SVD; Topic review for final.

*Reading*: 6.4.*Topic review for final exam**Final exam will be Wendesday, May 24, 10-12:30 in LBR 248.*

#### Thu 5/11: Singular Value Decomposition and Applications.

*Quiz 10 in class*: Covering problems from Sections 5.4, 6.3.*Reading*: 6.3, 6.4.*Homework*: Section 6.3: 3.1, 3.3, 3.4, 3.9, 3.10; Section 6.4: 4.1, 4.2, 4.4.

#### Tue 5/9: Polar decomposition and singular values.

*Reading*: Section 6.3.1-6.3.3.*Homework*: Section 6.3: #3.1, 3.2, 3.6, 3.7.

#### Thu 5/4: Least Squares for overdetermined systems.

*Lecture by Prof. Poimenidou**Reading*: Section 5.4*Homework*: Section 5.4: #4.1-4.4.

#### Thu 4/27: Exam 2.

*Exam 2 in class*

#### Tue 4/25: Review for Exam (and/or Least Squares).

*Exam 2*: will be in class on Thursday. It will cover material since the last exam:- Eigenvalues/vectors
- Similarity and diagonalization
- Inner products,
- Orthogonal vectors, projections, Gram-Schmidt
- Unitary transformations, unitary equivalence and unitary diagonalization.
- Self-adjoint and normal operators, and the spectral theorem.

- If Prof. Kottke is in, he will give an exam review. Otherwise, Prof. Poimenidou will lecture on Least Squares solutions for overdetermined linear systems.

#### Thu 4/20: Spectral Theorem for self adjoint and normal operators.

*Reading*: 6.2*Homework*: Section 6.2: #2.1-2.3, 2.6, 2.7, 2.13, 2.14.

#### Tue 4/18: Unitary equivalence and diagonalization, Schurâ€™s lemma.

*Reading*: 5.6, 6.1.*Homework*: Section 5.6: #6.1, 6.2, 6.6, 6.7; Section 6.1: #1.1.

#### Thu 4/13: Adjoints, Isometries and Unitary operators.

*Quiz 8 in class*: Covering problems from Sections 5.2, 5.3.*Reading*: 5.5, 5.6*Homework*: Section 5.5: 5.1-5.3, 5.6; Section 5.6: 6.4, 6.5.

#### Tue 4/11: Gram-Schmidt Process.

*Reading*: 5.3*Homework*: Section 5.3: #3.2, 3.3, 3.5-3.7, 3.10, 3.11.

#### Thu 4/6: Orthogonality and orthonormality.

*Quiz 7 in class*: Covering problems from Section 5.1.*Reading*: 5.2*Homework*: Section 5.2: #2.1-2.4

#### Tue 4/4: Inner Product Spaces.

*Reading*: 5.1*Homework*: Section 5.1: #1.1-1.5, 1.8.*Office Hours Today*: 3-4 instead of the usual 4-5.

#### Thu 3/23: LU Decomposition.

*Quiz 6 in class*: Covering problems from 4.2- Lecture will supplement the text, which does not cover LU decomposition.

#### Tue 3/21: Diagonalization.

*Reading*: 4.2.4-4.2.7.*Homework*: Section 4.2: #5, 10, 11, 12, 14.

#### Thu 3/16: Diagonalization.

*Quiz 5 in class*: Covering problems from Section 4.1.*Reading*: 4.2.1-4.2.4.*Homework*: Section 4.2: #1, 2, 3, 4, 6, 7, 8.

#### Tue 3/14: Eigenvalues.

*Reading*: 4.1*Homework*: 4.1: #1.1-1.3, 1.6, 1.10, 1.11.

#### Thu 3/9: Exam 1.

- Exam is on all material we have covered so far. (There will not be any problems about permutations.)

#### Tue 3/7: Cofactor expansion for determinants.

*Reading*: 3.5*Homework*: Section 3.5: #5.2, 5.4, 5.5 (Note: these will not appear on any quiz, but will give you practice for the midterm.)

#### Thu 3/2: Determinants continued.

*Quiz 4 in class*: covering homework from sections 2.6-2.8.*Reminder*: The first midterm exam will be next Thursday, 3/9.*Reading*: 3.4*Homework*: Section 3.4: #4.1, 4.3, 4.4.

#### Tue 2/28: Change of basis, similarity. Determinants.

*Reading*: 2.8, 3.1, 3.2.*Homework*: Section 2.8: #8.1-8.6; Section 3.3: #3.1-3.3.

#### Thu 2/23: Fundamental subspaces and rank.

*Quiz 3 in class*: covering material since last quiz.*Reading*: 2.6, 2.7.*Homework*: Section 2.6: #6.1, Section 2.7: #7.1-7.6.

#### Tue 2/21: Pivot analysis, dimension, finding inverses.

*Reading*: 2.3, 2.4, 2.5.*Homework*: Section 2.3: Exercises 3.1, 3.2, 3.4, 3.9; Section 2.4: Exercise 4.1; Section 2.5 Exercises 5.1, 5.3, 5.4.

#### Thu 2/16: Quiz 2 solutions.

#### Thu 2/16: Linear systems of equations and row reduction.

*Quiz 2 in class*: covering material since last quiz.*Reading*: 2.1, 2.2.*Homework*: Section 2.2: Excercises 2.1, 2.2

#### Tue 2/14: Invertibility, Isomorphisms, Subspaces.

*Reading*: 1.6, 1.7.*Homework*: Exercises 6.1, 6.5, 6.6, 6.8, 6.9, 6.12, 6.13, 7.1-7.4.

#### Thu 2/9: Quiz 1 solutions.

#### Thu 2/9: Linear transformations, matrix multiplication.

**Quiz 1 in class**: covering homework problems from last time.*Reading*: 1.3, 1.4, 1.5.*Homework*: Exercises 3.2-3.4, 3.6, 5.2-5.4, 5.6, 5.7.

#### Tue 2/7: Vector spaces, Bases.

*Reading*: 1.1, 1.2.*Homework*: all problems in 1.1 and 1.2.

We will have our first quiz Thursday on homework problems from 1.1 and 1.2.