Linear Algebra for Computer Scientists. 12. Introducing the Matrix
This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order
From playlist Linear Algebra for Computer Scientists
What is a matrix? Free ebook http://tinyurl.com/EngMathYT
From playlist Intro to Matrices
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
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
An introduction to how the jacobian matrix represents what a multivariable function looks like locally, as a linear transformation.
From playlist Multivariable calculus
Cayley-Hamilton Theorem: Example 1
Matrix Theory: We verify the Cayley-Hamilton Theorem for the real 3x3 matrix A = [ / / ]. Then we use CHT to find the inverse of A^2 + I.
From playlist Matrix Theory
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)
Gentle example showing how to compute the Jacobian. Free ebook http://tinyurl.com/EngMathYT
From playlist Several Variable Calculus / Vector Calculus
Hamiltonian Mechanics in 10 Minutes
In this video I go over the basics of Hamiltonian mechanics. It is the first video of an upcoming series on a full semester university level Hamiltonian mechanics series. Corrections -4:33 the lagrangian should have a minus sign between the first two terms, not a plus.
From playlist Summer of Math Exposition 2 videos
Calogero Particles and Fluids: A Review (Lecture 2) by Alexios Polychronakos
PROGRAM: INTEGRABLE SYSTEMS IN MATHEMATICS, CONDENSED MATTER AND STATISTICAL PHYSICS ORGANIZERS: Alexander Abanov, Rukmini Dey, Fabian Essler, Manas Kulkarni, Joel Moore, Vishal Vasan and Paul Wiegmann DATE : 16 July 2018 to 10 August 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore
From playlist Integrable systems in Mathematics, Condensed Matter and Statistical Physics
Andrei Bogdan Bernevig - Exact Eigenstates in Non-Integrable Systems: A violation of the ETH
We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to c
From playlist Quantum Encounters Seminar - Quantum Information, Condensed Matter, Quantum Field Theory
Quantum Metrology II by Girish Agarwal
Dates: Thursday 03 Jan, 2013 - Saturday 05 Jan, 2013 Venue: ICTS-TIFR, IISc Campus, Bangalore The school aims to provide students and researchers an introduction to the field of quantum information, computation and communication. Topics that will be covered include introduction to quantu
From playlist Mini Winter School on Quantum Information and Computation
Non-Equilibrium Steady States of Quantum Non-Hermitian Lattice Models by Aashish Clerk
PROGRAM NON-HERMITIAN PHYSICS (ONLINE) ORGANIZERS: Manas Kulkarni (ICTS, India) and Bhabani Prasad Mandal (Banaras Hindu University, India) DATE: 22 March 2021 to 26 March 2021 VENUE: Online Non-Hermitian Systems / Open Quantum Systems are not only of fundamental interest in physics a
From playlist Non-Hermitian Physics (ONLINE)
Jeongwan Haah - Nontrivial Clifford QCAs - IPAM at UCLA
Recorded 01 September 2021. Jeongwan Haah of Microsoft Research presents "Nontrivial Clifford QCAs" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Abstract: An interesting role of QCA is that it can disentangle a Hamiltonian while quantum circuits cannot. We
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter
Lec 14 | MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008
Lecture 14: Definition of angular momenta and Instructor: Robert Field http://ocw.mit.edu/5-80F08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008
Seth Lloyd - Quantum polar decomposition - IPAM at UCLA
Recorded 25 January 2022. Seth Lloyd of the Massachusetts Institute of Technology presents "Quantum polar decomposition" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: The polar decomposition decomposes a matrix into the product of a unitary and an Hermitian matrix. This ta
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
Chao Yang - Low rank approximation in electron excitation calculations - IPAM at UCLA
Recorded 02 May 2022. Chao Yang of Lawrence Berkeley National Laboratory presents "Low rank approximation in electron excitation calculations" at IPAM's Large-Scale Certified Numerical Methods in Quantum Mechanics Workshop. Abstract: A practical way to study electron excitation computation
From playlist 2022 Large-Scale Certified Numerical Methods in Quantum Mechanics
In this video, I calculate the determinant of a block matrix and show that the answer is what you expect, namely the product of the determinants of the blocks. This is useful for instance in the proof of the Cayley Hamilton theorem, but also in the theory of Jordan Forms. Cayley-Hamilton
From playlist Determinants
Topological quantum phases - Alexei Kitaev
Special Seminar Topic: Topological quantum phases Speaker: Alexei Kitaev Affiliation: California Institute of Technology; Distinguished Visiting Professor, School of Natural Sciences Date: November 25, 2019 For more video please visit http://video.ias.edu
From playlist Mathematics