CIS 610, Spring 2005

Advanced Geometric Methods in Computer Science

Some Slides and Notes

• Motivations, Problems and Goals   (slides, pdf)   |  (slides, ppt)   |  (slides, keynote)
• Spectral Theorems (Symmetric, Skew-Symmetric, Normal matrices)   (slides, ps)   |  (slides, pdf)
• Polar Form and SVD   (slides, ps)   |  (slides, pdf)
• Least Squares, SVD, Pseudo Inverse, PCA   (slides, ps)   |  (slides, pdf)
• Lie Groups and Lie Algebras, the exponential map, part I   (slides, ps)   |  (slides, pdf)
• Lie Groups and Lie Algebras, the exponential map, part II   (slides, ps)   |  (slides, pdf)
• Review of Groups and Group Actions, I   (slides, ps)   |  (slides, pdf)
• The Lorentz Groups O(n, 1), SO(n, 1), SO_0(n, 1), Topological Groups   (slides, ps)   |  (slides, pdf)
• Manifolds, Part II   (slides, ps)   |  (slides, pdf)
• Lie Groups and Lie Algebras, the exponential map, part III   (ps)   |  (pdf)
• Notes on Group Actions, Manifolds, Lie Groups and Lie Algebras   (html)
• On the Early History of the Singular Value Decomposition, by G.W. Stewart   (pdf)
• Lecture Notes on Differentiable Manifolds, Geometry of Surfaces, etc., by Nigel Hitchin   (html)
• An Introduction to Riemannian Geometry, by S. Gudmundsson   (html)
• Appendices I and II of Lectures on Matrices, by J.H.M Wedderburn (1937)   (pdf)
• Remarks on the Cayley representation of orthogonal matrices and
  on making matrices invertible by perturbing the diagonal   (ps)   |  (pdf)
• Bibliography (from book)   (ps)
• Clifford algebras, Clifford groups, and the groups Pin and Spin (notes)   (ps)   |  (pdf)
• Basics of Algebra and Analysis   (notes)