642:550 Linear Algebra and Applications (Fall, 2010) -- Syllabus

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

Date Lecture Reading Topics
9/1 1 1.4-5 Review of Matrix Algebra; Gaussian Elimination by Elementary Matrices
9/8 2 1.6 LU and LDU Factorizations; Matrix Inverses
9/13 3 2.1-2 Vector Spaces and Subspaces; Solving Linear Systems
9/15 4 2.3 Linear Independence, Basis, and Dimension;
Column space, null space, uniqueness of rref(A)
9/20 5 2.4, 2.6 Four Fundamental Subspaces; Linear Transformations and Their Matrices
      MATLAB Assignment # 1 due 9/20
9/22 6 3.1-2 Orthogonal Spaces; Inner Products and Projections
9/27 7 3.3 Projections and Least-squares Approximations
9/29 8 3.4 Orthonormal Bases; Gram-Schmidt Process; QR Factorization
10/4 9 4.1-2 Properties of the Determinant Function
10/6 10 4.2-3 Formulas for Determinants; Permutations
10/11 11 4.4 Determinant Formulas for Matrix Inverse; Cramer's Rule
10/13 12 5.1-2 Eigenvalues and Eigenvectors; Diagonalization
      MATLAB Assignment # 2 due 10/18
10/18 13 5.3-4 Difference and Differential Equations
10/20 14   Midterm Exam on Chapters 1-4 (closed book)
10/25 15 5.4, 5.5 Matrix Exponentials; Complex vector spaces; Hermitian matrices
10/27 16 5.6 Schur Triangular Form; Unitary Diagonalization of Normal Matrices
11/1 17 3.5, Notes Discrete Fourier Transform; Shift Operator and Circulant Matrices
11/3 18 3.5, Notes Diagonalization of Circulant Matrices; Fast Fourier Transform
      MATLAB Assignment # 3 due 11/8
11/8 19 5.6 Cayley-Hamilton Theorem; Canonical forms for matrices
11/10 20 5.6; App. B Jordan Canonical Form--Statement and Examples
11/15 21 App. B Proof of Jordan Canonical Form; Applications to Differential Equations
11/17 22 6.1-2 Quadratic Forms; Positive-definite Matrices
      MATLAB Assignment # 4 due 11/22
11/22 23 6.2 Indefinite Quadratic Forms; Law of Inertia
      NO CLASS November 24
11/29 24 6.3 Singular Value Decomposition
12/1 25 6.4 Minimum Principles; Rayleigh Quotient
12/6 26 7.2-3 Matrix Norm and Condition Number; Power Method
12/8 27 7.3 Hessenberg form and QR algorithm
      MATLAB Assignment # 5 due 12/13
12/13 28 7.3 QR algorithm and Inverse Power Method for eigenvectors
12/20 12-3   Final Exam (closed book)

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maintained by / Roe Goodman (goodman AT math DOT rutgers DOT edu) / Revised August 13, 2010