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 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.
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MondayFriday
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Week 114 January6.1 vector spaces6.1 properties of vector spaces6.2 linear dependence
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Week 221 January6.3 subspaces6.3 spans, 6.4 bases6.4 Steintz replacement theorem
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Week 328 January6.4 bases, 6.5 sums of subspaces6.5 dimensions of sums of subspaces6.5 direct sums of subspaces
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4 February
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Week 411 February6.5 complements, direct sums of more than 2 subspaces, 7.1 linear transformations 7.1 combining linear transformations, subspaces related to linear transformations7.1 rank nullity theorem
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Week 518 February7.2 coordinates for vectors, matrix representations of linear transformations7.2 how to use matrix representations7.3 change of bases
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Week 625 February8.1 diagonal and triangular form8.1 Cayley-Hamilton theorem, proof for diagonalisable matrices8.1 better proof of Cayley-Hamilton, minimal polynomial
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Week 74 Marchmidterm8.1 minimal polynomials of diagonalisable matrices, 8.2 what is Jordan form8.2 generalised eigenvectors
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Week 811 March8.3 Jordan form algorithm step 1, information from the Jordan form8.3 Jordan form algorithm step 28.3 Jordan form algorithm step 4
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Week 918 March9.1 linear forms9.3 dual of a linear transformation9.3 matrix of the dual transformation
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Week 1025 March9.2 change of dual bases9.2 the double dual, 9.4 bilinear forms9.4 matrix of a bilinear form, quadratic forms
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Week 111 April9.4 diagonalising a quadratic form, by row and column operations
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Week 128 April9.4 diagonalising a quadratic form9.5 definiteness of real quadratic forms10.1 inner products
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Week 1315 April10.1 orthogonal projections, Gram-Schmidt
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22 April10.1 Cauchy-Schwarz and triangle inequalities, orthogonal complement10.2 Riesz representation theorem
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optional class, 17 May:10.2 adjoint10.5 spectral theorem for normal operators