Introductory Linear Algebra (Summer 2020)

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Syllabus

Homework

• Homework 1 (revised on 5/27) is due 6/1 (Solution)
• Homework 2 (revised on 6/3) is due 6/7 (Solution, Office Hour Discussion)
• Homework 3 (revised on 6/10) is due 6/15 (Solution)
• Homework 4 is due 6/21 (Solution)
• Homework 5 (revised on 6/25) is due 6/29 (Solution)
• Homework 6 (revised on 6/30) is due 7/1 (Solution)

Reference

• Relevant sections of the textbook are listed under each lecture below. Note that we will take a different viewpoint and not follow the logical order of the textbook.
• Lecture Notes by Prof. Frederick P. Greenleaf (Caution: these notes are for a higher level course and covers a lot more materials than our class, but we will follow roughly the same logical order while skipping advanced topics).

Lectures

I will try to post workshop problems and lecture notes at least one day in advance. Details will be added to the notes during lectures and I will update them after each lecture. The workshop problems selected for submission are due the next day at noon.

• 5/26: Vector Spaces over R, C
  • Notes
  • Workshop 1 (Solution)
  • Relevant Sections in the Textbook: 7.1, 1.1
• 5/27: Subspaces of a Vector Space; Span of a Set of Vectors
  • Notes
  • Workshop 2 (Solution page 1, 2, 3)
  • Relevant Sections in the Textbook: 7.1, 4.1, 1.6
• 5/28: Linear Dependence and Linear Independence of a Set of Vectors
  • Notes
  • Workshop 3 (Solution, Office Hour Discussion)
  • Relevant Sections in the Textbook: 1.7
• 6/1: Bases and Dimension of a Vector Space; Matrices and Matrix Algebra; Definition of Invertibility of a Matrix
  • Short Videos to Watch before the Lecture:
    • Intro to Matrices
    • Operations with Matrices
    • How to Multiply Matrices
  • Notes: Part 1, Part 2
  • Workshop 4 (Solution)
  • Relevant Sections in the Textbook: 7.3, 4.2, 1.1, 2.1, 2.3
• 6/2: Partitioned Matrices and Block Multiplication; Linear Transformations and Their Matrices; Composition of Linear Transformations
  • Notes
  • Workshop 5 (Solution)
  • Relevant Sections in the Textbook: 2.5, 7.2, 7.4
• 6/3: Invertibility of Linear Transformations
  • Workshop 6 (Solution, Office Hour Discussion)
  • Relevant Sections in the Textbook: 7.4
• 6/4: Change of Basis; Kernel and Range of Linear Transformations
  • Notes
  • Workshop 7 (Solution: Method 1, 2)
  • Relevant Sections in the Textbook: 7.4
• 6/9: Reviewing Midterm 1
  • Notes
• 6/10: Elementary Row and Column Operations on Matrices; Elementary Matrices; Gaussian Elimination; Reduced Row Echelon Form of a Matrix
  • Notes
  • Workshop 9 (Solution page 1, 2, 3, 4)
  • Relevant Sections in the Textbook: 1.3, 1.4, 1.6, 1.7, 2.3
• 6/11: Dimension (Rank and Nullity) Theorem; Rank; Matrix Inversion Algorithm
  • Notes: Part 1, Part 2
  • Workshop 10 (Solution)
  • Relevant Sections in the Textbook: 1.4, 2.4
• 6/15: The Determinant
  • Short Video to Watch and Discuss during the Lecture
  • Notes
  • Workshop 11 (Solution)
  • Relevant Sections in the Textbook: 3.1, 3.2
• 6/16: More on Invertibility of Matrices; the Wronskian; Solutions to Homogeneous vs. Inhomogeneous Systems of Equations; Definitions of Eigenvectors and Eigenvalues
  • Notes
  • Workshop 12 (Solution)
  • Possibly Helpful Video
  • Relevant Sections in the Textbook: 5.1, 7.4
• 6/17: Computing Eigenvalues and Eigenvectors; the Characteristic Polynomial
  • Notes
  • Workshop 13 (Solution)
  • Relevant Sections in the Textbook: 5.2, 7.4
• 6/18: Diagnoliazation; Applications of the Eigen-thoery
  • Notes
  • Further Reading: "The $25,000,000,000 Eigenvector: The Linear Algebra behind Google" (You should have online access to this article through university library website)
  • Relevant Sections in the Textbook: 5.3, 5.4, 5.5
• 6/23: More on Google's PageRank Algorithm; Dot Product and Orthogonality
  • Short Video to Watch before Lecture
  • Notes
  • Workshop 14 (Solution)
  • Relevant Sections in the Textbook: 5.5, 6.1, 6.2
• 6/24: Gram-Schmit Process; Orthogonal Matrices
  • Notes
  • Workshop 15 (Solution)
  • Further Reading: Fourier Series--An Application of Orthonormal Basis, by David Speyer
  • Relevant Sections in the Textbook: 6.2, 6.5
• 6/25: Orthogonal Matrices; Orthogonal Complement and Projection
  • Notes
  • Workshop 16 (Solution)
  • Relevant Sections in the Textbook: 6.5, 6.3, 6.4
• 6/29: Least Squares and Inconsistent Equations; Diagonalization of Symmetric Matrices
  • Notes
  • Workshop 17 (Solution)
  • Relevant Sections in the Textbook: 6.4, 6.6
• 6/30: Singular Value Decomposition and Application in Image Processing; Reviewing Midterm 2
  • Notes Part 1, 2
  • Short Video to Watch during Lecture
  • Relevant Sections in the Textbook: 6.7
• 7/1: Review
  • Notes