CIS 515, Fall 2013
Some Course Notes and Slides
Notes
Basics of Algebra and Analysis (manuscript)
(html)
Fundamentals of Linear Algebra and Optimization; Some Notes
(pdf)
Applications of Scientific Computation; EAS205, Some Notes
(pdf)
Notes on Elementary Spectral Graph Theory
Applications to Graph Clustering Using Normalized Cuts
(pdf)
Logarithms and Square Roots of Real Matrices
(pdf)
Chapter 5 from GMA (2nd edition); Basics of Projective Geometry
(pdf)
Chapter 8 from GMA (first edition); The Quaternions and the Spaces
S^3, SU(2), SO(3), and RP^3
(pdf)
Slides
Some Matlab code
bezier-parabola
(m)
bezier-cubic
(m)
bezier function, degree 2
(m)
bezier function, degree 3
(m)
iterate1
(m)
iterate2
(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)
Talk(s)
Rotation Logic (talk given at the Robotics Symposium, Sept. 27, 2013)
(slides, pdf)
The Quaternions and the Spaces
S^3, SU(2), SO(3), and RP^3
(pdf)
Problems, Questions and Motivations; Vector Spaces, Bases, Linear Maps  
(slides, pdf)
Matrices and Linear Maps  
(slides, pdf)
Affine Maps, Direct Sums, The Dual Space, Duality  
(slides, pdf)
Gaussian, LU, and Choleski Decompositions  
(slides, pdf)
Determinants and Applications  
(slides, pdf)
Determinants "a la Michael Artin" (from EAS205)  
(slides, pdf)
Normed spaces and matrix norms; condition number of a matrix  
(slides, pdf)
Iterative Methods for Solving Linear Systems  
(slides, pdf)
Euclidean Spaces  
(slides, pdf)
QR-Decomposition for Arbitrary Matrices  
(slides, pdf)
Basics of Hermitian Geometry  
(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)
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