Spring 2013
  • MATH 323-503: Linear Algebra
    •

    Time and venue:   TR 12:45-2:00 p.m., BLOC 160

    First day hand-out

    Office hours (MILN 004):
  • Tuesday, 11:00 a.m.-12:30 p.m.
  • Thursday, 11:00 a.m.-12:30 p.m.
  • by appointment

    • Help sessions (BLOC 117):
  • Sunday - Thursday, 8:00-10:00 p.m.
    •
    Additional office hours (MILN 004):
  • Wednesday, May 1, 12:00-2:00 p.m.
  • Tuesday, May 7, 12:00-2:00 p.m.
  • Thursday, May 9, 12:00-2:00 p.m.
    •

    Final exam (with solutions)

    Final exam:  Wednesday, May 8, 8:00-10:00 a.m., BLOC 160

    Rules for the exam:  no books, no lecture notes, no calculators.  Bring paper and a stapler.

    Sample problems for the final exam (Solutions)

    Sample problems for Test 1 (Solutions)

    Sample problems for Test 2 (Solutions)

    Test 2 (with solutions)



    Quiz:  Tuesday, April 23 (topic: matrix exponentials) Quiz:  Tuesday, April 23  (solution)

    Homework assignments ##1-11

    Course outline:

    Part I: Elementary linear algebra

  • Systems of linear equations
  • Gaussian elimination, Gauss-Jordan reduction
  • Matrices, matrix algebra
  • Determinants

    Leon's book: Chapters 1-2

    Lecture 1: Systems of linear equations. Gaussian elimination.
  • Leon 1.1

    • Lecture 2: Gaussian elimination (continued). Row echelon form. Gauss-Jordan reduction.
  • Leon 1.1-1.2

    • Lecture 3: Row echelon form (continued). Applications of systems of linear equations. Matrix algebra.
  • Leon 1.2-1.3

    • Lecture 4: Matrix multiplication. Diagonal matrices. Inverse matrix.
  • Leon 1.3-1.5

    • Lecture 5: Inverse matrix (continued).
  • Leon 1.4-1.5

    • Lecture 6: Matrix algebra (continued). Determinants.
  • Leon 1.4-1.5, 2.1-2.2

    • Lecture 7: Determinants (continued).
  • Leon 2.1-2.3


    • Part II: Abstract linear algebra

  • Vector spaces
  • Linear independence
  • Basis and dimension
  • Coordinates, change of basis
  • Linear transformations

    Leon's book: Chapters 3-4

    Lecture 8: Vector spaces.
  • Leon 3.1

    • Lecture 9: Subspaces of vector spaces. Span. Spanning set.
  • Leon 3.2

    • Lecture 10: Spanning set (continued). Linear independence.
  • Leon 3.2-3.3

    • Lecture 11: Wronskian. Basis of a vector space. Dimension.
  • Leon 3.3-3.4

    • Lecture 12: Basis of a vector space (continued). Rank and nullity of a matrix.
  • Leon 3.2, 3.4, 3.6

    • Lecture 13: Review for Test 1.
  • Leon 1.1-1.5, 2.1-2.2, 3.1-3.4, 3.6

    • Lecture 14: Basis and coordinates. Change of basis. Linear transformations.
  • Leon 3.5, 4.1

    • Lecture 15: Linear transformations (continued). Range and kernel. General linear equations.
  • Leon 4.1

    • Lecture 16: Matrix transformations. Matrix of a linear transformation. Similarity of matrices.
  • Leon 4.2-4.3


    • Part III: Advanced linear algebra

  • Orthogonality
  • Inner products and norms
  • The Gram-Schmidt orthogonalization process
  • Eigenvalues and eigenvectors
  • Diagonalization

    Leon's book: Sections 5.1-5.6, 6.1, 6.3

    Lecture 17: Euclidean structure in Rn. Orthogonality. Orthogonal complement.
  • Leon 5.1-5.2

    • Lecture 18: Orthogonal projection. Least squares problems.
  • Leon 5.2-5.3

    • Lecture 19: Least squares problems (continued). Norms and inner products.
  • Leon 5.3-5.4

    • Lecture 20: Inner product spaces. Orthogonal sets.
  • Leon 5.4-5.5

    • Lecture 21: The Gram-Schmidt orthogonalization process.
  • Leon 5.5-5.6

    • Lecture 22: Eigenvalues and eigenvectors. Characteristic polynomial.
  • Leon 6.1

    • Lecture 23: Diagonalization. Review for Test 2.
  • Leon 6.3 (diagonalization); 3.5, 4.1-4.3, 5.1-5.6, 6.1, 6.3 (review for Test 2)


    • Part IV: Topics in applied linear algebra

  • Matrix exponentials
  • Rotations in space
  • Orthogonal polynomials

    Leon's book: Sections 5.5, 5.7, 6.1-6.4

    Lecture 24: Matrix polynomials. Matrix exponentials.
  • Leon 6.2-6.3

    • Lecture 25: Complexification. Orthogonal matrices. Rigid motions.
  • Leon 5.5, 6.4

    • Lecture 26: Orthogonal polynomials. Review for the final exam.
  • Leon 5.7 (orthogonal polynomials); 1.1-1.5, 2.1-2.2, 3.1-3.6, 4.1-4.3, 5.1-5.7, 6.1-6.3 (review for the final exam)