Date |
Topic |
Reading Assignment |
Homework Assignment |
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| Monday, January 12 |
Class meets with Prof. Schumacher to discuss Leslie Matrix Models |
Handout on Difference Eqns and Leslie Model. |
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| Wednesday, January 14 |
Further discussion of difference equations and Leslie Matrix Model
Review of raising matrices to powers
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| Friday, January 16 |
Leslie Matrices and long-term behavior |
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| Monday, January 19 |
Leslie Matrices and Long-term behavior, cont.
Review and extensions of Diagonalization. |
Finbeiner 7.1 and 7.2 |
Due: Homework on Leslie Matrices and Difference Equations |
| Wednesday, January 21 |
Eigenvector/Eigenvalue properties of Leslie Matrices. |
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| Friday, January 23 |
Eigenvector/Eigenvalue properties of Leslie Matrices, continued. |
Google Euler's formula and DeMoivre's theorem for complex numbers; see they are used to find powers of complex numbers. |
Due: Homework #2 on Leslie Matrices |
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| Monday, January 26 |
Finish discussion of Difference Equations and Leslie matrices. |
Finkbeiner 7.1 and 7.2 ---- AGAIN!!! Plus the first two pages of section 7.3. (If you see unfamiliar language or notation, you will need to dig back in the book to find and understand it---if there's no reference, use the index.) |
Homework: Write at least 3, but no more 5 specific questions from the reading---make sure to specify what portion of the reading you are asking about. (E.g. Having trouble understanding the proof of thm. 7.3; Or I don't understand that matrix P they keep talking about on pg.194.) |
| Wednesday, January 28 |
Digging into some review |
Diagonalization and change of basis |
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| Friday, January 30 |
Algebraic and geometric points of view for Linear transformations |
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Due: Solutions to Linear Difference Equations |
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| Monday, February 2 |
Decompositions with Linear Transformations, part I. |
Read end of Finkbeiner 7.2, AGAIN!!! |
Due: Finkbeiner---Problems 6.4-3, 7.1-4 and 7.1-7; Prove Theorems 7.1 and 7.2. |
| Wednesday, February 4 |
Developing some new ideas. |
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Due: Finkbeiner 7.2---Problems 8, 9 plus the handout on New Ideas. |
| Friday, February 6 |
Decompositions with Linear Transformations, cont. |
Read Finkbeiner, pages 203-204, again!! |
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| Monday, February 9 |
Decompositions with Linear Transformations, cont.
Class presentations of proofs. |
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Work on "Facts" associated with Decomposition thm. |
| Wednesday, February 11 |
A short primer on Direct Sums
Finish Decomposition Theorem.
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| Friday, February 13 |
T-cyclic subspaces of a vector space.
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Read Finkbeiner Pg 205. |
Work on Direct Sums and Nilpotent-NonSingular Decompositions homework |
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| Monday, February 16 |
Finish discussion of T-cyclic subspaces |
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Due: Direct Sums and Nilpotent-NonSingular Decompositions homework |
| Wednesday, February 18 |
Test # 1
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| Friday, February 20 |
Introduction to Singular Value Decomposition |
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| Monday, February 23 |
SVD intro, continued
Graham-Schmidt Process for constructing an orthonormal basis |
Read about Graham-Schmidt (This is the first three pages of Section 6.4 in Lay, but should also be in most linear algebra texts.) |
SVD Preliminaries hmwk due. |
| Wednesday, February 25 |
Finish Graham-Schmidt Discussion
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SVD Homework 1, due. |
| Friday, February 27 |
The Norm of a Linear Transformation and interpreting the SVD. |
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Graham-Schmidt homework due. |
Spring Break
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| Monday, March 16 |
Geometric interpretation of the SVD |
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| Wednesday, March 18 |
SVD---theoretical underpinnings |
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| Friday, March 20 |
Image of the unit sphere under a linear transformation. |
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| Monday, March 23 |
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Theoretical Issues and the SVD homework due. |
| Wednesday, March 25 |
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The SVD for Symmetric matrices homework, due. |
| Friday, March 27 |
No Class; Prof. Schumacher out of town.
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| Monday, March 30 |
The kth svd approximation as "best" rank k approximation of A. |
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| Wednesday, April 1 |
The kth svd approximation as "best" rank k approximation of A, cont. |
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Redo of problem # 3 from Theoretical Issues and the SVD homework due. |
| Friday, April 3 |
Exploring some properties of the best rank k approximation of A.
Introducing Project "Matrix Approximation and Image Processing."
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| Monday, April 6 |
Best rank k approximation and the Frobenius metric: Matrix Approximation and Image Processing, cont. |
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Exploring best rank k and Frobenius metric homework, due. |
| Wednesday, April 8 |
Work day on "Matrix Approximation and Image Processing." |
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| Friday, April 10 |
Ill-conditioned matrices---square, invertible matrices |
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| Monday, April 13 |
Ill-conditioned matrices and the svd |
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| Wednesday, April 15 |
Review of the svd |
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Matrix Approximation and Image Processing Project, due by 4 p.m. |
| Friday, April 17 |
Test # 2 |
Homework on ill-conditioned matrices and the svd. |
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| Monday, April 20 |
3D and the svd---project # 2. |
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| Wednesday, April 22 |
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| Friday, April 24 |
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| Monday, April 27 |
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| Wednesday, April 29 |
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| Friday, May 1 |
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Thursday, May 7 from 6:30-9:30 p.m.