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Schedule for weeks 1 through 16 |
| Wk |
Day |
Date |
Topic | Resources | Events |
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| 1 | Mon | Jan 06 | Course Introduction
ℝn, ℂn | Chapter 1.A | Problems 1, 3, 5, 8, 13 | |
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| Wed | Jan 08 | Vector Spaces | Chapter 1.B | Problems 1, 2, 4, 5 | |
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| Fri | Jan 10 | Subspaces | Chapter 1.C | Problems 1, 4, 5, 10, 12, 15, 16, 18, 19, 21, 22
HW 1 due |
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| 2 | Mon | Jan 13 | Span
Linear Independence | Chapter 2.A | Problems 1, 5, 6, 8, 9, 10, 11, 12, 13
HW 2 due | |
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| Wed | Jan 15 | Bases | Chapter 2.B | Problems 1, 3, 5, 6, 7
HW 3 due | |
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| Fri | Jan 17 | Dimension | Chapter 2.C | Problems 3, 4, 6, 10, 11, 12, 13, 17
HW 4 due |
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| 3 | Mon | Jan 20 | Linear Maps | Chapter 3.A
(Re-read the proof of 3.5 until you fully understand it.) | Problems 1, 3, 4, 5, 6, 7, 10
HW 5 due | |
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| Wed | Jan 22 | Null Spaces and Ranges | Chapter 3.B
(Re-read the proof of 3.22 until you fully understand it.) | Problems 3, 5, 6, 9, 11, 12, 14, 17, 21
Note: Write basis vectors of Rn as e1, ..., en instead of (1,0,...,0), etc.
HW 6 due | |
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| Fri | Jan 24 | Null Space and Range | Chapter 3.B | HW 5 and HW 6 redo due |
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| 4 | Mon | Jan 27 | Matrices | Chapter 3.C
(Put some thought into the motivation for matrix multiplication on pages 74-75.) | Problems 2, 3, 4, 7, 12, 13, 15
HW 7 due | |
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| Wed | Jan 29 | Invertibility and Isomorphic Vector Spaces | Chapter 3.D | Problems 1, 2, 7, 8, 10, 11
HW 8 due | |
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| Fri | Jan 31 | Products of Vector Spaces | Chapter 3.E (through page 93) | Problems 2, 3, 6
HW 9 due |
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| 5 | Mon | Feb 03 | | | No class due to illness | |
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| Wed | Feb 05 | Polynomials | Chapter 4 | Problems: 1, 2, 3, 4, 7
No HW due today! | |
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| Fri | Feb 07 | Chapter 1-3 | Book
Notes | Test 1 |
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| 6 | Mon | Feb 10 | Winter Recess | | No Class | |
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| Wed | Feb 12 | Invariant Subspaces | Chapter 5.A (ignore quotient stuff) | Problems 1, 2, 3, 4, 6, 9, 11
No HW due again! | |
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| Fri | Feb 14 | Eigenvalues and Eigenvectors | Chapter 5.A | Problems 15, 19, 21, 23, 26
HW 10 due |
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| 7 | Mon | Feb 17 | Eigenvectors and Upper-Triangular Matrices | Chapter 5.B | Problems 1, 2, 3, 4, 6
HW 11 due | |
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| Wed | Feb 19 | More Eigenstuff | Chapter 5.B | Problems 10, 14, 15
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| Fri | Feb 21 | Eigenspaces and Diagonal Matrices | Chapter 5.C | Problems 1, 2, 3, 6
HW 12 due |
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| 8 | Mon | Feb 24 | Finish Eigenspaces, Diagonal Matrices | Chapter 5.C | Problems 8, 9, 11
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| Wed | Feb 26 | Inner Products and Norms | Chapter 6.A | Problems 1, 2, 4, 5 (Assume V is finite dimensional), 7, 8, 10 | |
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| Fri | Feb 28 | Inner Products and Norms | Chapter 6.A | Problems 12, 13, 14, 16, 18 (Change x and y on the right to |x| and |y|), 22, 24, 31
HW 13 due |
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| 9 | Mon | Mar 02 | Orthonormal Bases | Chapter 6.B | Problems 1, 2, 3, 5 and 6
HW 14 due | |
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| Wed | Mar 04 | Orthonormal Bases | Chapter 6.B | Problem 8, 10, 14 | |
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| Fri | Mar 06 | Orthogonal Complements and Minimization Problems | Chapter 6.C | Problems 1, 2, 3, 5, 9
HW 15 due |
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| 10 | Mon | Mar 09 | Orthogonal Complements and Minimization Problems | Chapter 6.C | Problems 9, 10
HW 16 due | |
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| Wed | Mar 11 | Chapters 1-6 | | HW 17 due
Test 2 | |
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| Fri | Mar 13 | Spring Break! | | No Class |
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Spring Break Week |
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| 11 | Mon | Mar 23 | Adjoint | Chapter 7.A (pages 204-208) | Problems 1, 2, 3, 5 | |
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| Wed | Mar 25 | Self-Adjoint and Normal Operators | Chapter 7.A (pages 209-214) | Problems
7: Bethany
8: Eric
9: Kam
12: Merideth
13: Brandon
16: Liam | |
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| Fri | Mar 27 | The Spectral Theorem | Chapter 7.B | HW 18 due
Problems
1: Adam
2: Kam
3: Marideth
4, 5: Bethany
6: Brandon
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| 12 | Mon | Mar 30 | | Chapter 7.B | HW 19 due
Problems
7: Eric
8: Adam
9: Liam | |
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| Wed | Apr 01 | Positive Operators
Isometries | Chapter 7.C | HW 20 due
Problems:
1: Merediθ
2: Kam
3: Bethany
4: Eric
5: Brandon
6: Liam
7: Adam | |
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| Fri | Apr 03 | Polar Decomposition
Singular Value Decomposition | Chapter 7.D | Problems
1: Eric (Hint: See Example 7.4)
3: Liam
4: Brandon
5: Bethany
7: Maredith (Hint: Find √(T*T) and then determine what S must be)
8: Kam
10:Adam |
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| 13 | Mon | Apr 06 | Generalized Eigenvectors
Nilpotent Operators | Chapter 8.A (pages 241-247) | HW 21 due
Problems
1: Bethany
2: Adam (Hint: See Example 5.8A)
3: MarryDeath
4: Kam
5: Eric
16: Brandon
17: Liam | |
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| Wed | Apr 08 | | Chapter 8.A (pages 248-249) | HW 22 due
Problems
18: MareOfDeath
6: Liam
7: Brandon (Don't forget to prove that 0 IS an eigenvector)
8: Adam
9: Bethany
13: Eric (Hint: use a homework problem to help)
14: Kam (Hint: This is really simple if you use the proper earlier results) | |
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| Fri | Apr 10 | Good Friday | | No Class |
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| 14 | Mon | Apr 13 | Easter Weekend | | No Class | |
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| Wed | Apr 15 | Decomposition of an Operator | Chapter 8.B | Problems
1: Kam
2: Brandon
4: Meredeth
5: Bethany
6: Adam
8: Eric | |
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| Fri | Apr 17 | Characteristic and Minimal Polynomials | Chapter 8.C | HW 23 due
Problems
1: Bethany
2: Eric
3: Adam
5: Kam
7: Merudyth (typo in problem: T should be P)
8: Liam
11: Brandon
16: Liam |
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| 15 | Mon | Apr 20 | Characteristic and Minimal Polynomials | Chapter 8.C | HW 24 due | |
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| Wed | Apr 22 | Jordan Form | Chapter 8.D | Problems
1
2
3
6 | |
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| Fri | Apr 24 | Everything | | Review |
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| Ex | Tue | Apr 28 | | | Final Exam 12:30-2:30pm |
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