In electromagnetism, a branch of fundamental physics, the matrix representations of the Maxwell's equations are a formulation of Maxwell's equations using matrices, complex numbers, and vector calculus. These representations are for a homogeneous medium, an approximation in an inhomogeneous medium. A matrix representation for an inhomogeneous medium was presented using a pair of matrix equations. A single equation using 4 × 4 matrices is necessary and sufficient for any homogeneous medium. For an inhomogeneous medium it necessarily requires 8 × 8 matrices. (Wikipedia).
Using a Matrix Equation to Solve a System of Equations
This video shows how to solve a system of equations by using a matrix equation. The graphing calculator is integrated into the lesson. http://mathispower4u.yolasite.com/ http://mathispower4u.wordpress.com/
From playlist Matrix Equations
Understanding Matrices and Matrix Notation
In order to do linear algebra, we will have to know how to use matrices. So what's a matrix? It's just an array of numbers listed in a grid of particular dimensions that can represent the coefficients and constants from a system of linear equations. They're fun, I promise! Let's just start
From playlist Mathematics (All Of It)
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Ex: Write a System of Equations as a Matrix Equation (3x3)
This video explains how to write a matrix equation for a system of three equations with three unknowns. http://mathispower4u.com
From playlist Matrix Equations
Ex 2: Solve a System of Two Equations Using a Matrix Equation
This video explains how to solve a system of two linear equations with two unknowns using a matrix equation. Site: http://mathispower4u Blog: http://mathispower4u.wordpress.com
From playlist Matrix Equations
QED Prerequisites: The Dirac Equation
In this lesson we give an introduction to the discovery and logic of the Dirac Equation. We introduce the notion of a 4-component spinor field and Dirac Matrices. We do not start developing a solution for this equation, or for the Klein Gordon equation either. There is much more to say abo
From playlist QED- Prerequisite Topics
In this video, we'll learn how to view a complex number as a 2x2 matrix with a special form. We'll also see that there is a matrix version for the number 1 and a matrix representation for the imaginary unit, i. Furthermore, the matrix representation for i has the defining feature of the im
From playlist Complex Numbers
Ch7Pr38: Matrix Representation Theorem
This video answers four questions regarding properties of a linear transformation, its image, rank and nullity. This is Chapter 7 Problem 38 from the MATH1231/1241 Algebra notes. Presented by Dr Thomas Britz from the UNSW School of Mathematics and Statistics.
From playlist Mathematics 1B (Algebra)
Differential Equations | Homogeneous System of Differential Equations Example 2
We solve a homogeneous system of linear differential equations with constant coefficients using the matrix exponential. In this case the associated matrix is 2x2 and not diagonalizable. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Systems of Differential Equations
Advice for Research Mathematicians | The joy of maxel number theory: Chebyshev Polys 2 | Wild Egg
We extend our newish approach to families of orthogonal polynomials / polynumbers involving creating two dimensional arrays, or maxels, from them to the case of the Chebyshev polynomials of the second kind. These are very important in representation theory of Lie groups and Lie algebras,
From playlist Maxel inverses and orthogonal polynomials (non-Members)
Patrick Joly: Long time behaviour of the solution of Maxwell’s equations in dissipative Lorentz...
CONFERENCE Recorded during the meeting " Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials " the May 25, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video a
From playlist Numerical Analysis and Scientific Computing
Bartomeu Fiol - Radiation from Matrix Models
I give an overview of work characterizing radiation in generic four-dimensional conformal field theories. I argue that for theories with conformal scalars, the radiated energy is not positive definite and the radiated power is not Lorentz invariant. I then determine the coupling dependence
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Wall Crossing, Part 1 - Greg Moore
Wall Crossing, Part 1 Greg Moore Rutgers, The State University of New Jersey July 27, 2010
From playlist PiTP 2010
Katharina Kormann: A geometric electromagnetic particle in cell method on staggered grids
Recorded during the meeting "Numerical Methods for Kinetic Equations 'NumKin21' " the June 15, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit A kinetic description of a plasma in external and self-consistent fields is given by the
From playlist Numerical Analysis and Scientific Computing
Calculating the matrix of a linear transformation with respect to a basis B. Here is the case where the input basis is the same as the output basis. Check out my Vector Space playlist: https://www.youtube.com/watch?v=mU7DHh6KNzI&list=PLJb1qAQIrmmClZt_Jr192Dc_5I2J3vtYB Subscribe to my ch
From playlist Linear Transformations
Lars Andersson - Geometry and analysis in black hole spacetimes (Part 3)
Black holes play a central role in general relativity and astrophysics. The problem of proving the dynamical stability of the Kerr black hole spacetime, which is describes a rotating black hole in vacuum, is one of the most important open problems in general relativity. Following a brief i
From playlist Ecole d'été 2014 - Analyse asymptotique en relativité générale
Solving a System of Equations with a Matrix Equation
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Quick video on how to solve a system of equations with matrix equation.
From playlist Systems of Equations
Lecture 5 | New Revolutions in Particle Physics: Standard Model
(February 8, 2010) Professor Leonard Susskind discusses gauge theories. This course is a continuation of the Fall quarter on particle physics. The material will focus on the Standard Model of particle physics, especially quantum chromodynamics (the theory of quarks) and the electroweak th
From playlist Lecture Collection | Particle Physics: Standard Model