Concept
Degeneracy (mathematics)
Related lectures (30)
Convex Functions: Elementary Concepts
Introduces elementary concepts of convex functions, including hulls, transformations, conditions, and examples.
Solving Linear Programs: SIMPLEX Method
Explains the SIMPLEX method for solving linear programs and optimizing the solution through basis variable manipulation.
Convex Optimization: Elementary Results
Explores elementary results in convex optimization, including affine, convex, and conic hulls, proper cones, and convex functions.
Quadratic Forms and Symmetric Bilinear Forms
Explores quadratic forms, symmetric bilinear forms, and their properties.
Linear Programming Basics
Covers the basics of linear programming and the simplex method, focusing on finding optimal solutions and handling degeneracy.
Intersection Numbers: Algebraic Counting Solutions
Explores intersection numbers for counting solutions to polynomial equations algebraically and their geometric significance in intersection theory and enumerative geometry.
Division in Extreme and Mean Ratio: DEMR
Explores Division in Extreme and Mean Ratio (DEMR) for geometric constructions and its historical significance in art and architecture.
Conic Sections & Gnomonics
Explores the historical use of conic sections and gnomonics in ancient sundials and astronomical instruments.
Pseudo-Euclidean Spaces: Isometries and Bases
Explores pseudo-Euclidean spaces, emphasizing isometries and bases in vector spaces with non-degenerate quadratic forms.
Symmetries of Regular Polyhedra
Explores the historical background and significance of symmetries in regular polyhedra, shedding new light on Euclid's Elements.