CIS 515, Fall 2020
Some Course Notes and Slides
Notes
Basics of Algebra and Analysis (manuscript)
(html)
Linear Algebra and Optimization With Applications to Machine Learning,
Vol. I and II
(html)
Linear Algebra and Optimization With Applications to Machine Learning,
Vol. I, pages vii to 566.
(pdf)
Linear Algebra and Optimization With Applications to Machine Learning,
Vol. I, pages 567 to 808.
(pdf)
Linear Algebra and Optimization With Applications to Machine Learning,
Vol. II, pages vii to 558.
(pdf)
Linear Algebra and Optimization With Applications to Machine Learning,
Vol. II, pages 559 to 879.
(pdf)
Applications of Scientific Computation; EAS205, Some Notes
(pdf)
Spectral Theory of Unsigned and Signed Graphs
Applications to Graph Clustering: a Survey
(pdf)
Logarithms and Square Roots of Real Matrices
(pdf)
Chapters 1, 2, 3, 4
on Mathematical Reasoning and Logic, functions, relations,
from "Discrete Mathematics, Second Edition:"
(pdf)
Chapter 5 from GMA (2nd edition); Basics of Projective Geometry
(pdf)
Chapter 9 from GMA (2nd edition); The Quaternions and the Spaces
S^3, SU(2), SO(3), and RP^3
(pdf)
Chapter 10 from GMA (2nd edition); Dirichlet-Voronoi Diagrams and
Delaunay Triangulations
(pdf)
Slides
Some Matlab code
bezier-parabola
(m)
bezier-cubic
(m)
bezier function, degree 2
(m)
bezier function, degree 3
(m)
Lemniscate
(m)
Solving a triangular system by backsubstitution, v1
(m)
Solving a triangular system by backsubstitution, v2
(m)
Solving a triangular system; some examples
(m)
Computes a point on a curve using de Casteljau's algorithm
(m)
Linear (affine!) interpolation
(m)
To display the construction of a point using de Casteljau's algorithm
(m)
Running de Casteljau's algorithm; examples
(m)
The Steiner Roman surface
(m)
Problems, Questions and Motivations; Vector Spaces, Bases, Linear
Maps, The dual space  
(slides, pdf)
Matrices and Linear Maps  
(slides, pdf)
Haar Bases and Haar Wavelets  
(slides, pdf)
Direct Sums, Affine Maps  
(slides, pdf)
Determinants and Applications  
(slides, pdf)
Determinants "a la Michael Artin"  
(slides, pdf)
Gaussian, LU, and Choleski Decompositions  
(slides, pdf)
Normed spaces and matrix norms; condition number of a matrix  
(slides, pdf)
Iterative Methods for Solving Linear Systems  
(slides, pdf)
The Dual Space, Duality  
(slides, pdf)
Euclidean Spaces  
(slides, pdf)
QR-Decomposition for Arbitrary Matrices  
(slides, pdf)
Hermitian Spaces  
(slides, pdf)
Eigenvectors and Eigenvalues  
(slides, pdf)
Spectral Theorems in Euclidean and Hermitian Spaces  
(slides, pdf)
Introduction to the Finite Elements Method  
(slides, pdf)
Singular Value Decomposition (SVD) and Polar Form  
(slides, pdf)
Applications of SVD and Pseudo-Inverses  
(slides, pdf)
Quadratic Optimization Problems  
(slides, pdf)
Basic Notions of Topology  
(slides, pdf)
Review of Multivariate Calculus  
(slides, pdf)
Derivatives (Directional, Total), Series  
(slides, pdf)
Slides on the spectral theory of unsigned and signed graphs
with applications to graph clustering
Graphs and graph Laplacians  
(slides, pdf)
Spectral Graph Drawing  
(slides, pdf)
Graph Clustering using Normalized Cuts; 2 clusters  
(slides, pdf)
Graph Clustering using Normalized Cuts; K clusters  
(slides, pdf)
Graph Clustering using Normalized Cuts; Finding a discrete solution  
(slides, pdf)
Signed Graphs ;  
(slides, pdf)
Graph Clustering Using Ratio Cuts  
(slides, pdf)
Appendix; Rayleigh Ratios, Rayleigh-Ritz Theorem,
Courant-Fischer Theorem  
(slides, pdf)
Other slides
Rotation Logic (talk given at the Robotics Symposium, Sept. 27, 2013)
(slides, pdf)
Some Mathematical Methods in Machine Learning
(Two lectures (each 1h 25mn)
given in Paris at ENS Cachan, Sept. 8, 2020)
(slides, pdf)
Dirichlet-Voronoi Diagrams and
Delaunay Triangulations
(pdf)
The Quaternions and the Spaces
S^3, SU(2), SO(3), and RP^3
(pdf)
Back to
Gallier Homepage
published by: