Math 310, Applied Linear Algebra - Spring 2019

Instructor: Vahan Huroyan

Email: vahanhuroyan (at) math (dot) arizona (dot) edu

Section Time: MWF 8:00 - 8:50

Section Room: Biological Sciences West, Rm 210

Office Hours: GS 721, WF 10:00-11:00, Mathematics 220, F 2:00-3:00

Course Syllabus: [here]

Textbook: Applied Linear Algebra second edition, by Peter J. Olver and Chehrzad Shakiban.

Extra Reading: Introduction to Applied Linear Algebra - Vectors, Matrices, and Least Squares, by Stephen Boyd and Lieven Vandenberghe.

Announcements:

  • Lecture 1, Jan. 9: Solution of Linear Systems and Introduction to Matrices and Vectors (Section 1.1, Section 1.2)
  • Lecture 2, Jan. 11: Gaussian elimination and LU factorization (Section 1.3)
  • Lecture 3, Jan. 14: Gaussian elimination and LU factorization, Pivoting and Permutations (Section 1.3, Section 1.4)
  • Lecture 4, Jan. 16: Pivoting and Permutations (Section 1.4)
  • Lecture 5, Jan. 18: Matrix Inverses (Section 1.5)
  • Lecture 6, Jan. 23: Matrix Inverses (Section 1.5)
  • Lecture 7, Jan. 25: QUIZ 1 ([quiz 1 solutions] ), Transpose and symmetric matrices (Section 1.6)
  • Lecture 8, Jan. 28: Review
  • Lecture 9, Jan. 30: Midterm 1 ([Midterm 1 solutions]
  • Lecture 10, Feb. 1: General Linear Systems (Section 1.8)
  • Lecture 11, Feb. 4: General Linear Systems, Determinants (Section 1.8, Section 1.9)
  • Lecture 12, Feb. 6: Vector Spaces (Section 2.1)
  • Lecture 13, Feb. 8: Vector Spaces, Subspaces (Section 2.1, Section 2.2)
  • Lecture 14, Feb. 11: Subspaces (Section 2.2)
  • Lecture 15, Feb. 13: Span and Linear Independence (Section 2.3)
  • Lecture 16, Feb. 15: Basis and Dimension (Section 2.4)
  • Lecture 17, Feb. 18: Basis and Dimension (Section 2.4)
  • Lecture 18, Feb. 20: QUIZ 2 ([quiz 2 solutions] ), The Fundamental Matrix Subspaces (Section 2.5)
  • Lecture 19, Feb. 22: The Fundamental Matrix Subspaces (Section 2.5)
  • Lecture 20, Feb. 25: Review
  • Lecture 21, Feb. 27: Midterm2 ([Midterm 2 solutions]
  • Lecture 22, March 1: The Fundamental Matrix Subspaces (Section 2.5)
  • Lecture 23, March 11: Inner Products (Section 3.1)
  • Lecture 24, March 13: Inner Products (Section 3.1)
  • Lecture 25, March 15: Inequalities (Section 3.2)
  • Lecture 26, March 18: Norms (Section 3.3)
  • Lecture 27, March 20: Positive Definite Matrices (Section 3.4)
  • Lecture 28, March 22: Positive Definite Matrices (Sections 3.4)
  • Lecture 29, March 25: QUIZ 3 ([quiz 3 solutions], Completing the Square, The Cholesky Factorization (Section 3.5)
  • Lecture 30, March 27: Orthogonal and Orthonormal Bases (Section 4.1)
  • Lecture 31, March 29: The Gram Schmidt Process (Section 4.2)
  • Lecture 32, April 1: Review
  • Lecture 33, April 3: Midterm 3 ([Midterm 3 solutions]
  • Lecture 34, April 5: The Gram Schmidt Process (Section 4.2)
  • Lecture 35, April 8: Orthogonal Matrices (Section 4.3)
  • Lecture 36, April 10: Orthogonal Matrices (The QR Factorization) (Section 4.3)
  • Lecture 37, April 12: Orthogonal Matrices, Householder's method (Section 4.3)
  • Lecture 38, April 15: Orthogonal Projections (Section 4.4)
  • Lecture 39, April 17: Eigenvalues and Eigenvectors (Section 8.2)
  • Lecture 40, April 19: Complex Eigenvalues and Eigenvectors (Section 8.2)
  • Lecture 41, April 22: Eigenvector Bases, Diagonalizable matrices (Section 8.3)
  • Lecture 42, April 24: Quiz 4 ([quiz 4 solutions], Eigenvalues of Symmetric Matrices (Section 8.5)
  • Lecture 43, April 26: Optimization Principles for Eigenvalues of Symmetric Matrices (Section 8.5), Singular Value Decomposition (Section 8.7)
  • Lecture 44, April 29: Power Method (Section 9.5), Review
  • Lecture 45, May 1: Review

    • Homework:

  • HW 1: posted 1/11, due 1/18 ---- 1.2.13, 1.2.20, 1.2.22, 1.2.23, 1.2.37, 1.3.7, 1.3.14, 1.3.20, 1.3.22, 1.3.27, 1.3.29
  • HW 2: posted 1/23, due 2/6 ---- 1.3.33 (a, d, f), 1.4.1 (f), 1.4.21 (a, c, e), 1.5.1 (c), 1.5.9 (b, d), 1.5.20 (a, b), 1.5.23 (a, b), 1.5.25 (b, d, h), 1.5.34 (a, d)
  • HW 3: posted 2/6, due 2/20 ---- 1.6.3, 1.6.4, 1.6.5, 1.6.11, 1.6.14 (a, b), 1.6.26, 1.8.2 (a, d, f), 1.8.4, 1.8.17, 1.8.19, 1.9.2, 1.9.5, 1.9.9, 1.9.19, 1.9.21
  • HW 4: posted 2/18, due NA ---- 2.1.8, 2.1.9, 2.1.13, 2.2.1, 2.2.7, 2.2.9, 2.2.17, 2.2.18, 2.3.1, 2.3.4, 2.3.9, 2.3.21 (a, e, g, h), 2.3.23, 2.4.3, 2.4.4, 2.4.16
  • HW 5: posted 3/18, due 4/1 ---- 2.5.2 (e, f), 2.5.3, 2.5.14, 2.5.24 (a, d), 2.5.25, 3.1.1, 3.1.4, 3.1.5, 3.1.11, 3.1.12, 3.1.17, 3.1.23, 3.2.9, 3.2.22, 3.2.29, 3.3.3, 3.3.8, 3.3.16, 3.3.26, 3.3.51
  • HW 6: posted 4/9, due 4/19 ---- 3.4.8, 3.4.13, 3.4.23, 3.4.29, 4.1.2, 4.1.5, 4.1.14, 4.2.3, 4.2.6 (a, b), 4.2.17 (a, c)
  • HW 7: REVIEW, suggested problems ---- 1.3.2, 1.3.4, 1.3.21, 1.3.33, 1.4.21, 1.5.25, 1.5.31, 1.5.33, 1.6.25, 2.2.4, 2.2.8, 2.2.9, 2.3.2, 2.3.4, 2.3.21, 2.3.25, 2.3.26, 2.4.1, 2.4.2, 2.4.15, 2.5.1, 2.5.2, 2.5.7, 2.5.13, 3.1.2, 3.1.4, 3.2.1, 3.2.5, 3.3.2, 3.3.11, 3.3.45, 3.4.1, 3.4.22, 3.4.29, 4.1.1, 4.1.2, 4.2.1, 4.2.3, 4.2.6, 4.2.9, 4.2.17, 4.3.1, 4.3.20, 4.3.27, 4.3.34, 8.2.1, 8.2.5, 8.3.2, 8.3.13, 8.3.17