MATH 503 Home Page

• Thursday, 18
  Sections 0.1-0.3 - Linear Algebra vs. Numerical Linear Algebra
  Sections 1.1-1.2 - Vectors, vector spaces, linear independence, basis, dimension, orthogonality
  
  
  

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• Tuesday, 23
  Questions about Homework #1
  
• Thursday, 25
  Questions about Homework #2
  Sections 1.3.1-1.3.6 - Matrices, determinants, inverses, range and null space, eigenvalues, orthogonality and projections
  Homework #1 Due
  Homework #2 Due
  
  
  

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• Tuesday, 30
  Sections 1.3.6-1.3.7 - Orthogonality and projections, orthogonal decomposition of a vector
  Special factorizations of n x n matrices - Diagonalization (P^-1AP = D), unitary diagonalization (Q^*AQ = D), Schur triangularization (Q^*AQ = R)
  Homework #3 Due
  

• Thursday, 1
  Sections 1.4-1.6 - Special matrices, Cayley-Hamilton Theorem, singular values
  
  
  

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• Tuesday, 6
  Go over Homework #1
  Homework #4 Due
  
• Thursday, 8
  Questions about Homeworks #5, 6
  Go over Homeworks #2, 3
  
  
  

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• Tuesday, 13
  Go over Homework #4
  Homework #5 Due
  Homework #6 Due
  
• Thursday, 15
  Inner products and norms
  Sections 1.7.1-1.7.2 - Vector and matrix norms
  
  
  

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• Tuesday, 20
  Questions about Homework #7
  Sections 1.7.3-1.7.4 - Vector and matrix convergence and norms of inverses
  Section 1.8 - Norm invariance of orthogonal matrices
  Homework #7 Due
  
• Thursday, 22
  Go over Homework #5
  
  
  

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• Tuesday, 27
  Go over Homeworks #6, 7
  

• Thursday, 1
  Briefly discuss Chapters 2 and 3
  Sections 8.1-8.2.1 - Eigenvalues and eigenvectors
  
  
  

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• Tuesday, 6
  Sections 8.2.2 - Eigenvalues and eigenvectors
  
• Thursday, 8
  Midterm Exam
  
  
  

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• Tuesday, 13
  No Class - Spring Break
• Thursday, 15
  No Class - Spring Break
  
  

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• Tuesday, 20
  Go over midterm exam
  Sections 8.2.1-8.2.2 - Eigenvalues and eigenvectors and Schur's Theorem
  
• Thursday, 22
  Sections 8.2.2-8.2.3 - Applications of Schur's Theorem and Jordan form
  
  
  

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• Tuesday, 27
  Section 8.3.1 - Eigenvalue problems and differential equations
  
• Thursday, 29
  Sections 8.4.1-8.4.2 - Gerschgorin's Theorems and eigenvalue bounds
  
  
  

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• Tuesday, 3
  Section 8.4.3 - Inertia of a matrix
  Sections 8.5.1-8.5.3 - Power method, Rayleigh quotient
  Homework #8 Due
  
• Thursday, 5
  Section 8.5.4 - Householder deflation
  Section 8.6-8.7 - Bauer-Fike Theorem
  Section 8.9 - Real Schur form
  Homework #9 Due
  
  
  

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• Tuesday, 10
  Section 8.11 - Symmetric eigenvalue problem
  
• Thursday, 12
  Kronecker product
  Homework #10 Due
  
  
  

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• Tuesday, 17
  Kronecker sum
  Homework #11 Due
  
• Thursday, 19
  Sylvester's equation
  Homework #12 Due
  
  
  

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• Tuesday, 24
  Go over Homework #10
  Homework #13 Due
  
• Thursday, 26
  Sections 9.1-9.2 - Generalized eigenvalue problem
  Sections 9.5 - Symmetric definite generalized eigenvalue problem
  Homework #14 Due
  
  
  

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• Tuesday, 1
  Section 10.1-10.3 - Singular Value Decomposition and eigenvalues
  Homework #15 Due
  
• Thursday, 3
  Section 10.6 - Properties of the SVD
  Section 10.8 - SVD and the pseudoinverse
  
  
  

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Homework and tests

• Read Sections 1.1-1.9
• Sections 1.2-1.3, #2, 10, 11
• Sections 1.4-1.6, #23, 24, 25a,b, 26, 30, 31a,b,f, 32, 34
• Sections 1.7-1.8, #36a, 39, 41a, 43a, 44, 46, 49, 55c

Homework #1, Math 221 review Due Thursday 1-25

Homework #2, Elementary True-False Due Thursday 1-25

Homework #3, Chapter 1, #2, 10, 11 Due Tuesday 1-30

Homework #4, Chapter 1, #23, 24, 25a,b, 26, 30, 31a,b,f, 32, 34 Due Tuesday 2-6

Homework #5, Math 333 review, omit #6, 8, 11, 12, 20, 21 Due Tuesday 2-13

Homework #6, Intermediate True-False, omit #2, 8-14, 17, 20, 25, 29, 31, 32 Due Tuesday 2-13

Homework #7, Chapter 1, #36a, 39, 41a, 43a, 44, 46, 49, 55c Due Tuesday 2-20

Midterm Exam, Chapter 1 Thursday 3-8

Chapter 8 Homework

• Read Sections 8.1-8.12
• Section 8.4, #4a-d,f, 5, 6, 7
• Section 8.5, #9
• Sections 8.6-8.8, #18, 19a-d, 21

Homework #8, Chapter 8, #4a-d,f 5, 6, 7 Due Tuesday 4-3

Homework #9, True-False, omit #4, 7, 13, 18, 20-22, 25, 30 Due Thursday 4-13

Homework #10, Chapter 8, #9, 18, 19a-d, 21 Due Thursday 4-12

Homework #11, True-False, #4, 12, 17, 20-24 Due Tuesday 4-17

Homework #12, True-False, #22-24, 26, 28 Due Thursday 4-19

Homework #13, Kronecker product handout Due Tuesday 4-24

Chapter 9 Homework

• Read Sections 9.1-9.2, 9.5
• Section 9.1, #1
• Section 9.2, #8
• Sections 9.5, #26

Homework #14, Chapter 9, #1, 8, 26, Prove Sherman-Morrison formula Due Thursday 4-26

Chapter 10 Homework

• Read Sections 10.1-10.3, 10.6, 10.8
• Sections 10.2-10.3, #1
• Section 10.6, #6a(first matrix in 5), 7b-c
• Section 10.8, #13, 14, 17(P₁, P₂)

Homework #15, Chapter 10, #1, 6a(first matrix in 5), 7b-c, 13, 14, 17(P₁, P₂) Due Tuesday 5-1