642:550 Linear Algebra and Applications (Fall, 2011) -- 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
9/07 1 1.4-5 Review of Matrix Algebra; Gaussian Elimination by Elementary Matrices
9/08 2 1.6 LU and LDU Factorizations; Matrix Inverses
9/12 3 2.1-2 Vector Spaces and Subspaces; Solving Linear Systems
9/14 4 2.3 Linear Independence, Basis, and Dimension;
Column space, null space, uniqueness of rref(A)
9/19 5 2.4, 2.6 Four Fundamental Subspaces; Linear Transformations and Their Matrices
      MATLAB Assignment # 1 due 9/19
9/21 6 3.1-2 Orthogonal Spaces; Inner Products and Projections
9/26 7 3.3 Projections and Least-squares Approximations
9/28 8 3.4 Orthonormal Bases; Gram-Schmidt Process; QR Factorization
10/3 9 4.1-2 Properties of the Determinant Function
10/5 10 4.2-3 Formulas for Determinants; Permutations
10/10 11 4.4 Determinant Formulas for Matrix Inverse; Cramer's Rule
10/12 12 5.1-2 Eigenvalues and Eigenvectors; Diagonalization
      MATLAB Assignment # 2 due 10/17
10/17 13 5.3-4 Difference and Differential Equations
10/19 14   Midterm Exam on Chapters 1-4 (closed book)
10/24 15 5.4, 5.5 Matrix Exponentials; Complex vector spaces; Hermitian matrices
10/26 16 5.6 Schur Triangular Form; Unitary Diagonalization of Normal Matrices
10/31 17 3.5, Notes Discrete Fourier Transform; Shift Operator and Circulant Matrices
11/02 18 3.5, Notes Diagonalization of Circulant Matrices; Fast Fourier Transform
      MATLAB Assignment # 3 due 11/07
11/07 19 5.6 Cayley-Hamilton Theorem; Canonical forms for matrices
11/09 20 5.6; App. B Jordan Canonical Form--Statement and Examples
11/14 21 App. B Proof of Jordan Canonical Form; Applications to Differential Equations
11/16 22 6.1-2 Quadratic Forms; Positive-definite Matrices
      MATLAB Assignment # 4 due 11/21
11/21 23 6.2 Indefinite Quadratic Forms; Law of Inertia
      NO CLASS November 23
11/28 24 6.3 Singular Value Decomposition
11/30 25 6.4 Minimum Principles; Rayleigh Quotient
12/05 26 7.2-3 Matrix Norm and Condition Number; Power Method
12/07 27 7.3 Hessenberg form and QR algorithm
      MATLAB Assignment # 5 due 12/12
12/12 28 7.3 QR algorithm and Inverse Power Method for eigenvectors
12/19 12-3   Final Exam (closed book)

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maintained by / Roe Goodman (goodman AT math DOT rutgers DOT edu) / Revised July 26, 2011