Textbook: Linear Algebra, by K. Hoffman and R. Kunze
| Aug 18 | Equivalent System of Linear Equations, Row-Reduced Echelon Matrices, Invertible Matrices |
| Aug 20 | Vector Saces, Subspaces, bases and Dimension |
| Aug 23 | Linear Transformations of Vector Saces, Representation of Transformation by Matrices |
| Aug 25 | Linear Functionals, the Algebra of Linear Transformations, Isomorphism, Transpose of a Linear Transformation |
| Aug 27 | The Dual of a Vector Space, the double dual |
| Aug 30 - Sept 1 | Review of Exercises |
| Sept 3 | Test # 1 |
| Sept 8 | The Algebra of Polynomials, Lagrange Interpolation. |
| Sept 10 | Polynomial Ideals, The Prime Factorization of a Polynomial |
| Sept 13 | Determinants Functions |
| Sept 15 | Permutations and Uniqueness f Determinants |
| Sept 20 | Multilinear Functions |
| Sept 22 | Elementary Canonical Forms, Eigenvalues (or Characteristic Values), Eigenvectors |
| Sept 24 | Invariant Subspaces |
| Sept 27 | Simultaneous Triangulation, Simultaneous Diagonalization, Invariant Direct Sums. |
| Sept 29 | Review of Exercises |
| Oct 1 | Test # 2 |
| Oct 4 | The Primary Decomposition Theorem |
| Oct 6 | The Rational and Jordan Forms |
| Oct 11 | Cyclic Decompositions and the Rational Form |
| Oct 13 | Cayley-Hamilton Theorem, Jordan Form |
| Oct 15 | Computation of Invariant Factors |
| Oct 18-20 | Review of Chapter 7 |
| Oct 22 | Test #3 |
| Oct 25 | Inner Product Spaces, cauchy-Schwarz Inequality |
| Oct 27 | Gram-Schmidt Orthogonalization Process, Bessel's Inequality |
| Oct 29 | Linear Functionals and Adjoints |
| Nov 1 | Unitary Operators |
| Nov 3 | Normal Operators |
| Nov 5 | Operators on Inner Product Spaces |
| Nov 8 | Positive Forms |
| Nov 10 | Spectral Theory |
| Nov 12 | Polar Decomposition of an Operator |
| Nov 15-17 | Review of Exercises |
| Nov 19 | Test #4 |
| Nov 22 | Bilinear Forms |
| Nov 29 | Symmetric Bilinear Forms |
| Dec1-3 | Review |