Math 3407 Advanced Linear Algebra Spring 2019 schedule  click to see board pictures from each lecture.
Note that the current syllabus has major changes from this version.

  Monday  Friday 
Week 1  14 January  6.1 vector spaces  6.1 properties of vector spaces  6.2 linear dependence 
Week 2  21 January  6.3 subspaces  6.3 spans, 6.4 bases  6.4 Steintz replacement theorem 
Week 3  28 January  6.4 bases, 6.5 sums of subspaces  6.5 dimensions of sums of subspaces  6.5 direct sums of subspaces 
 4 February    
Week 4  11 February  6.5 complements, direct sums of more than 2 subspaces, 7.1 linear transformations  7.1 combining linear transformations, subspaces related to linear transformations  7.1 rank nullity theorem 
Week 5  18 February  7.2 coordinates for vectors, matrix representations of linear transformations  7.2 how to use matrix representations  7.3 change of bases 
Week 6  25 February  8.1 diagonal and triangular form  8.1 CayleyHamilton theorem, proof for diagonalisable matrices  8.1 better proof of CayleyHamilton, minimal polynomial 
Week 7  4 March  midterm  8.1 minimal polynomials of diagonalisable matrices, 8.2 what is Jordan form  8.2 generalised eigenvectors 
Week 8  11 March  8.3 Jordan form algorithm step 1, information from the Jordan form  8.3 Jordan form algorithm step 2  8.3 Jordan form algorithm step 4 
Week 9  18 March  9.1 linear forms  9.3 dual of a linear transformation  9.3 matrix of the dual transformation 
Week 10  25 March  9.2 change of dual bases  9.2 the double dual, 9.4 bilinear forms  9.4 matrix of a bilinear form, quadratic forms 
Week 11  1 April  9.4 diagonalising a quadratic form, by row and column operations   
Week 12  8 April  9.4 diagonalising a quadratic form  9.5 definiteness of real quadratic forms  10.1 inner products 
Week 13  15 April  10.1 orthogonal projections, GramSchmidt   
 22 April   10.1 CauchySchwarz and triangle inequalities, orthogonal complement  10.2 Riesz representation theorem 
 optional class, 17 May:   10.2 adjoint  10.5 spectral theorem for normal operators 