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, Schur’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.