642:550 Linear Algebra and Applications (Fall, 2013) -- Syllabus

Text: Gilbert Strang, Linear Algebra and its Applications, Fourth Edition
    ISBN 0-03-010567-6, Thomson -- Brooks/Cole, 2006.

Date Lecture Reading Topics
9/04 1 1.4-5 Review of Matrix Algebra; Gaussian Elimination by Elementary Matrices
9/09 2 1.6 LU and LDU Factorizations; Matrix Inverses
9/11 3 2.1-2 Vector Spaces and Subspaces; Solving Linear Systems
9/16 4 2.3 Linear Independence, Basis, and Dimension;
Column Space, Null Space, Uniqueness of rref(A)
9/18 5 2.4, 2.6 Four Fundamental Subspaces; Linear Transformations and Their Matrices
      MATLAB Assignment # 1 due 9/23
9/23 6 3.1-2 Orthogonal Spaces; Inner Products and Projections
9/25 7 3.3 Projections and Least-squares Approximations
9/30 8 3.4 Orthonormal Bases; Gram-Schmidt Process; QR Factorization
10/02 9 4.1-2 Properties of the Determinant Function
10/07 10 4.2-3 Formulas for Determinants; Permutations
10/09 11 4.4 Determinant Formulas for Matrix Inverse; Cramer's Rule
      MATLAB Assignment # 2 due 10/14
10/14 12 5.1-2 Eigenvalues and Eigenvectors; Diagonalization
10/16 13 5.3-4 Difference and Differential Equations
10/21 14   Midterm Exam on Chapters 1-4 (closed book)
10/23 15 5.4, 5.5 Matrix Exponentials; Complex Vector Spaces; Hermitian Matrices
10/28 16 5.6 Schur Triangular Form; Unitary Diagonalization of Normal Matrices
10/30 17 3.5, Notes Discrete Fourier Transform; Shift Operator and Circulant Matrices
      MATLAB Assignment # 3 due 11/04
11/04 18 3.5, Notes Diagonalization of Circulant Matrices; Fast Fourier Transform
11/06 19 5.6 Cayley-Hamilton Theorem; Canonical forms for matrices
11/11 20 5.6; App. B Jordan Canonical Form--Statement and Examples
11/13 21 App. B Proof of Jordan Canonical Form; Applications to Differential Equations
      MATLAB Assignment # 4 due 11/18
11/18 22 6.1-2 Quadratic Forms; Positive-definite Matrices
11/20 23 6.2 Indefinite Quadratic Forms; Law of Inertia
11/25 24 6.3 Singular Value Decomposition
      NO CLASS November 27
12/02 25 6.4 Minimum Principles; Rayleigh Quotient
12/04 26 7.2-3 Matrix Norm and Condition Number; Power Method
      MATLAB Assignment # 5 due 12/09
12/09 27 7.3 Hessenberg form and QR algorithm
12/11 28 7.3 QR algorithm and Inverse Power Method for Eigenvectors
12/16 12-3   Final Exam (closed book)

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maintained by / Roe Goodman (goodman AT math DOT rutgers DOT edu) / Revised July 31, 2013