In graph theory, a branch of mathematics, a cycle basis of an undirected graph is a set of simple cycles that forms a basis of the cycle space of the graph. That is, it is a minimal set of cycles that allows every even-degree subgraph to be expressed as a symmetric difference of basis cycles. A fundamental cycle basis may be formed from any spanning tree or spanning forest of the given graph, by selecting the cycles formed by the combination of a path in the tree and a single edge outside the tree. Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time. In planar graphs, the set of bounded cycles of an embedding of the graph forms a cycle basis. The minimum weight cycle basis of a planar graph corresponds to the Gomory–Hu tree of the dual graph. (Wikipedia).
Dual basis definition and proof that it's a basis In this video, given a basis beta of a vector space V, I define the dual basis beta* of V*, and show that it's indeed a basis. We'll see many more applications of this concept later on, but this video already shows that it's straightforwar
From playlist Dual Spaces
Determine the Basis for a Set of Four Vectors in R3
This video explains how to determine the basis of a set of vectors in R3. https://mathispower4u.com
From playlist Linear Independence and Bases
11.4.1 The Unit Basis Vectors, One More Time
11.4.1 The Unit Basis Vectors, One More Time
From playlist LAFF Week 11
From playlist Linear Algebra Ch 8 (updated Jan2021)
From playlist Linear Algebra Ch 8 (updated Jan2021)
Introduction to Change of Basis Between Two Nonstandard Bases
This video introduces a change of basis and show how to convert between two nonstandard bases.
From playlist Vectors: Change of Basis
Linear Algebra - Lecture 31 - Coordinate Systems
In this video, I review the definition of basis, and discuss the notion of coordinates of a vector relative to that basis. The properties of a basis of a subspace guarantee that a vector in that subspace can be written as a linear combination of the basis vectors in only one way. The wei
From playlist Linear Algebra Lectures
Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! Basis for a Set of Vectors. In this video, I give the definition for a apos; basis apos; of a set of vectors. I think proceed to work an example that shows thr
From playlist Linear Algebra
Victor-Emmanuel Brunel: Learning Determinantal point processes from moments and cycles
Recording during the "Meeting in Mathematical Statistics" the December 21, 2017 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics
From playlist Probability and Statistics
Computing Homology Cycles with Certified Geometry - Tamal Dey
Computing Homology Cycles with Certified Geometry Tamal Dey Ohio State University March 7, 2012
From playlist Members Seminar
A tale of two bases - Anne Dranowski
Short Talks by Postdoctoral Members Topic: A tale of two bases Speaker: Anne Dranowski Affiliation: Member, School of Mathematics Date: September 23, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Determine the Basis for a Set of Four Vectors in R3
This video explains how to determine the basis of a set of vectors in R3.
From playlist Linear Independence and Bases
Circuits, Graph Theory, and Linear Algebra | #some2
This is a submission for the Summer of Math Exposition #2 by Peter C and Akshay S, who are high school students interested in math. Spiritual enthusiasm result from https://www.youtube.com/watch?v=eyuNrm4VK2w The crux of this video was motivated by Gilbert Strang's textbook on linear alg
From playlist Summer of Math Exposition 2 videos
Oliver Schlotterer: Moduli space integrals in string tree level amplitudes
The lecture was held within the framework of the Hausdorff Trimester Program: Periods in Number Theory, Algebraic Geometry and Physics.
From playlist Workshop: "Amplitudes and Periods"
Masha Vlasenko: Gamma functions, monodromy and Apéry constants
Abstract: In 1978 Roger Apéry proved irrationality of zeta(3) approximating it by ratios of terms of two sequences of rational numbers both satisfying the same recurrence relation. His study of the growth of denominators in these sequences involved complicated explicit formulas for both vi
From playlist Algebraic and Complex Geometry
Bertrand Eynard - 4/4 Topological Recursion, from Enumerative Geometry to Integrability
https://indico.math.cnrs.fr/event/3191/ Topological recursion (TR) is a remarkable universal recursive structure that has been found in many enumerative geometry problems, from combinatorics of maps (discrete surfaces), to random matrices, Gromov-Witten invariants, knot polynomials, confor
From playlist Bertrand Eynard - Topological Recursion, from Enumerative Geometry to Integrability
Character Tables for S4 and A4
Representation Theory of Finite Groups: We build the character tables for S4 and A4 from scratch. As an application, we use irreducible characters to decompose a tensor product.
From playlist Representation Theory
Quick Review Part B Simplicial Complexes - Damiano - 2020
Quick Review Part B Simplicial Complexes This lecture introduces simplicial homology mod 2 using mod 2 vector spaces. The chain vector spaces, boundary homomorphism, boundaries, cycles and homologies are presented and examples are provided. The homology vector spaces in each dimension are
From playlist Applied Topology - David Damiano - 2020
We learned about how vectors can form a basis for a vector space, and we can express any vector within a vector space as a linear combination of the basis vectors. But there can be more than one set of basis vectors. What if we want to express a vector using some other basis rather than th
From playlist Mathematics (All Of It)