Cayley-Hamilton Theorem: General Case
Matrix Theory: We state and prove the Cayley-Hamilton Theorem over a general field F. That is, we show each square matrix with entries in F satisfies its characteristic polynomial. We consider the special cases of diagonal and companion matrices before giving the proof.
From playlist Matrix Theory
In this video I show you how to prove Cayley's theorem, which states that every group is isomorphic to a permutation group. This video is a bit long because I take the time to revisit all the concepts required in the proof. these include isomorphisms, injective, surjective, and bijective
From playlist Abstract algebra
Cayley-Hamilton Theorem Example 2
Matrix Theory: Let A be the 3x3 matrix A = [1 2 2 / 2 0 1 / 1 3 4] with entries in the field Z/5. We verify the Cayley-Hamilton Theorem for A and compute the inverse of I + A using a geometric power series.
From playlist Matrix Theory
Calculus - The Fundamental Theorem, Part 1
The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.
From playlist Calculus - The Fundamental Theorem of Calculus
What are Connected Graphs? | Graph Theory
What is a connected graph in graph theory? That is the subject of today's math lesson! A connected graph is a graph in which every pair of vertices is connected, which means there exists a path in the graph with those vertices as endpoints. We can think of it this way: if, by traveling acr
From playlist Graph Theory
Jeffrey Winicour - Multi-Messenger Aspects of Characteristic Evolution - IPAM at UCLA
Recorded 7 October 2021. Jeffrey Winicour of the University of Pittsburgh presents "Multi-Messenger Aspects of Characteristic Evolution at IPAM's Workshop I: Computational Challenges in Multi-Messenger Astrophysics. Abstract: I review the characteristic evolution of coupled gravitational
From playlist Workshop: Computational Challenges in Multi-Messenger Astrophysics
Anna Sakovich - Positivity of mass for asymptotically hyperbolic initial data sets - IPAM at UCLA
Recorded 25 October 2021. Anna Sakovich of Uppsala University presents "Positivity of mass for asymptotically hyperbolic initial data sets" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: We will be concerned with asymptotically hyperbolic 'hyperboloidal
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
Robert Wald - The Memory Effect and Infrared Divergences - IPAM at UCLA
Recorded 27 October 2021. Robert Wald of the University of Chicago presents "The Memory Effect and Infrared Divergences" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: The "memory effect" is the permanent relative displacement of test particles after th
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
Pythagorean Theorem IV (visual proof; Garfield's trapezoid)
This is a short, animated visual proof of the Pythagorean theorem (the right triangle theorem) using the trapezoid that is now attributed to President James Garfield. This theorem states the square of the hypotenuse of a right triangle is equal to the sum of squares of the two other side l
From playlist Pythagorean Theorem
Lydia BIERI - The Einstein Equations and Gravitational Radiation
In Mathematical General Relativity (GR) the Einstein equations describe the laws of the universe. This system of hyperbolic nonlinear pde has served as a playground for all kinds of new problems and methods in pde analysis and geometry. A major goal in the study of these
From playlist Trimestre "Ondes Non Linéaires" - May Conference
Self-force and radiation reaction in general relativity by Adam Pound ( Lecture 3 )
PROGRAM SUMMER SCHOOL ON GRAVITATIONAL WAVE ASTRONOMY ORGANIZERS : Parameswaran Ajith, K. G. Arun and Bala R. Iyer DATE : 15 July 2019 to 26 July 2019 VENUE : Madhava Lecture Hall, ICTS Bangalore This school is part of the annual ICTS summer schools on gravitational-wave (GW) astronomy.
From playlist Summer School on Gravitational Wave Astronomy -2019
Visual Proof of Pythagoras' Theorem
More resources available at www.misterwootube.com
From playlist Pythagoras’ Theorem
Lectures on compactness in the ̄∂–Neumann problem (Lecture 2) by Emil Straube
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature
In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932
From playlist Algebra
Group theory 2: Cayley's theorem
This is lecture 2 of an online mathematics course on group theory. It describes Cayley's theorem that every abstract group is the group of symmetries of something, and as examples shows the Cayley graphs of the Klein 4-group and the symmetric group on 3 points.
From playlist Group theory
Katy Clough - Simulating fundamental fields in strong gravity environments - IPAM at UCLA
Recorded 27 October 2021. Katy Clough of the Queen Mary University of London presents "Simulating fundamental fields in strong gravity environments: opportunities and challenges" at IPAM's Workshop II: Mathematical and Numerical Aspects of Gravitation. Abstract: Whilst stationary, asymptot
From playlist Workshop: Mathematical and Numerical Aspects of Gravitation
Low-Excitation & High-Excitation Radio Galaxies: by Martin Hardcastle
Extragalactic Relativistic Jets: Cause and Effect PROGRAM LINK: www.icts.res.in/program/ERG2015 DATES: Monday 12 Oct, 2015 - Tuesday 20 Oct, 2015 VENUE: Ramanujan Lecture Hall, ICTS Bangalore DESCRIPTION : Active Galactic Nuclei (AGN) are the luminous centers of galaxies that are belie
From playlist Extragalactic Relativistic Jets: Cause and Effect
Have you ever wondered why the divergence theorem doesn't apply to line integrals? That's because the definition of the line integral is somewhat flawed! In this video, I generalize the notion of a surface integral so that it can be applied to line integrals (I call this a line-surface i
From playlist Multivariable Calculus
Ex: Determine the Distance Between Two Points Using the Pythagorean Theorem
This video explains how to determine the distance between two points on the coordinate plane using the Pythagorean Theorem. http://mathispower4u.com
From playlist Using the Pythagorean Theorem
Prince Charles Visits Bondi Beach (1966)
Prince Charles the Duke of Edinburgh arrives at Bondi Beach, Australia and meets a Guard of Honour of Lifesavers. Click here for more videos about Prince Charles: https://www.youtube.com/playlist?list=PL3kG3TM8jFKgx04WBg837FkYYhxxqMsgC Date found in the old record - 05/06/1966. 90,000 h
From playlist PRINCE CHARLES