Spring 2012
  • MATH 423-200/500: Linear Algebra II
  • Time and venue:   MWF 12:40-1:30 p.m., BLOC 160

    First day hand-out

    Office hours (MILN 004):
  • MWF 11:00 a.m.-12:00 p.m.
  • by appointment

  • Additional office hours (MILN 004):
  • Wednesday, May 2, 11:00 a.m.-1:00 p.m.
  • Thursday, May 3, 11:00 a.m.-1:00 p.m.
  • Monday, May 7, 12:00-3:00 p.m.

  • Homework assignments ##1-11


    Quiz 1:  Friday, April 13  (solution)
    Quiz 2:  Friday, April 20  (solutions)
    Quiz 3:  Friday, April 27  (solution)


    Final exam (with solutions)

    Sample problems for the final exam (Solutions)


    Sample problems for Test 1 (Solutions)
    Test 1 (with solutions)

    Sample problems for Test 2 (Solutions)
    Test 2 (with solutions)


    Course outline:

    Lecture notes:

    Lecture 1: Classical vectors. Vector space.
  • Friedberg/Insel/Spence 1.1-1.2

  • Lecture 2: Vector spaces: examples and basic properties.
  • Friedberg/Insel/Spence 1.2

  • Lecture 3: Subspaces of vector spaces. Review of complex numbers. Vector space over a field.
  • Friedberg/Insel/Spence 1.3, appendix C, appendix D

  • Lecture 4: Span. Spanning set. Linear independence.
  • Friedberg/Insel/Spence 1.3-1.5

  • Lecture 5: Linear independence (continued).
  • Friedberg/Insel/Spence 1.5

  • Lecture 6: Basis and dimension.
  • Friedberg/Insel/Spence 1.6-1.7

  • Lecture 7: Linear transformations. Range and null-space.
  • Friedberg/Insel/Spence 2.1

  • Lecture 8: Subspaces and linear transformations. Basis and coordinates. Matrix of a linear transformation.
  • Friedberg/Insel/Spence 2.1-2.2

  • Lecture 9: Matrix of a linear transformation (continued). Matrix multiplication.
  • Friedberg/Insel/Spence 2.2-2.3

  • Lecture 10: Inverse matrix. Change of coordinates.
  • Friedberg/Insel/Spence 2.3-2.5

  • Lecture 11: Change of coordinates (continued). Isomorphism of vector spaces.
  • Friedberg/Insel/Spence 2.4-2.5

  • Lecture 12: Review for Test 1.
  • Friedberg/Insel/Spence 1.1-1.7, 2.1-2.5, appendices C and D

  • Lecture 13: Advanced constructions of vector spaces.
  • Friedberg/Insel/Spence 1.3(exercises)

  • Lecture 14: General linear equations. Elementary matrices.
  • Friedberg/Insel/Spence 3.1

  • Lecture 15: Inverse matrix (continued). Transpose of a matrix.
  • Friedberg/Insel/Spence 3.2

  • Lecture 16: Rank of a matrix. Systems of linear equations. Reduced row echelon form.
  • Friedberg/Insel/Spence 3.2-3.4

  • Lecture 17: Reduced row echelon form (continued). Determinant of a matrix.
  • Friedberg/Insel/Spence 3.3-3.4, 4.1

  • Lecture 18: Determinants (continued).
  • Friedberg/Insel/Spence 4.1-4.4

  • Lecture 19: More on determinants.
  • Friedberg/Insel/Spence 4.2-4.5

  • Lecture 20: Geometry of linear transformations. Eigenvalues and eigenvectors. Characteristic polynomial.
  • Friedberg/Insel/Spence 4.1, 5.1

  • Lecture 21: Eigenvalues and eigenvectors (continued). Diagonalization.
  • Friedberg/Insel/Spence 5.1-5.2

  • Lecture 22: Diagonalization (continued). Matrix polynomials.
  • Friedberg/Insel/Spence 5.2

  • Lecture 23: Diagonalization (continued). The Cayley-Hamilton theorem.
  • Friedberg/Insel/Spence 5.2, 5.4

  • Lecture 24: Multiple eigenvalues. Invariant subspaces. Markov chains.
  • Friedberg/Insel/Spence 5.2-5.4

  • Lecture 25: Markov chains (continued). The Cayley-Hamilton theorem (continued).
  • Friedberg/Insel/Spence 5.3-5.4

  • Lecture 26: Review for Test 2.
  • Friedberg/Insel/Spence 3.1-3.4, 4.1-4.5, 5.1-5.4

  • Lecture 27: Norms and inner products.
  • Friedberg/Insel/Spence 6.1

  • Lecture 28: Inner product spaces.
  • Friedberg/Insel/Spence 6.1

  • Lecture 29: Orthogonal sets.
  • Friedberg/Insel/Spence 6.2

  • Lecture 30: The Gram-Schmidt process. Orthogonal complement.
  • Friedberg/Insel/Spence 6.2

  • Lecture 31: Dual space. Adjoint operator.
  • Friedberg/Insel/Spence 2.6, 6.3

  • Lecture 32: Adjoint operator (continued). Normal operators.
  • Friedberg/Insel/Spence 6.3-6.4

  • Lecture 33: Diagonalization of normal operators.
  • Friedberg/Insel/Spence 6.4

  • Lecture 34: Unitary operators. Orthogonal matrices.
  • Friedberg/Insel/Spence 6.4-6.5

  • Lecture 35: Orthogonal matrices (continued). Rigid motions. Rotations in space.
  • Friedberg/Insel/Spence 6.5, 6.11

  • Lecture 36: Operator of orthogonal projection.
  • Friedberg/Insel/Spence 6.6

  • Lecture 37: Jordan blocks. Jordan canonical form.
  • Friedberg/Insel/Spence 7.1-7.2

  • Lecture 38: Generalized eigenvectors. Jordan canonical form (continued).
  • Friedberg/Insel/Spence 7.1-7.2

  • Lecture 39: Review for the final exam.
  • Friedberg/Insel/Spence 1.1-1.7, 2.1-2.5, 3.1-3.4, 4.1-4.5, 5.1-5.4, 6.1-6.6, 6.11, 7.1-7.2