Dipole Matrix Element Explained
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From playlist Optoelectronic and Photonic Devices
Sets might contain an element that can be identified as an identity element under some binary operation. Performing the operation between the identity element and any arbitrary element in the set must result in the arbitrary element. An example is the identity element for the binary opera
From playlist Abstract algebra
This video discusses unitary matrix transformations and how they relate to the geometry of the singular value decomposition (SVD). These lectures follow Chapter 1 from: "Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz Amazon: h
From playlist Data-Driven Science and Engineering
A set might contain many inverse elements under some binary operation. To have such an element, this set must also contain an identity element under the binary operation in question. An element is an inverse element of another element in a set if performing the binary operation between t
From playlist Abstract algebra
Abstract Algebra | Irreducibles and Primes in Integral Domains
We define the notion of an irreducible element and a prime element in the context of an arbitrary integral domain. Further, we give examples of irreducible elements that are not prime. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Personal Website: http://
From playlist Abstract Algebra
Representation Theory: We explain unitarity and invariant inner products for representations of finite groups. Full reducibility of such representations is derived. Course materials, including problem sets and solutions, available at http://mathdoctorbob.org/UR-RepTheory.html
From playlist Representation Theory
How do we add matrices. A matrix is an abstract object that exists in its own right, and in this sense, it is similar to a natural number, or a complex number, or even a polynomial. Each element in a matrix has an address by way of the row in which it is and the column in which it is. Y
From playlist Introducing linear algebra
Definition of a Group and Examples of Groups
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Group and Examples of Groups
From playlist Abstract Algebra
Operator Scaling via Geodesically Convex Optimization, Invariant Theory... - Yuanzhi Li
Optimization, Complexity and Invariant Theory Topic: Operator Scaling via Geodesically Convex Optimization, Invariant Theory and Polynomial Identity Testing Speaker: Yuanzhi Li Affiliation: Princeton University Date: June 7. 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX
Lie Groups and Lie Algebras: Lesson 11 - The Classical Groups Part IX In this lecture we count the degrees of freedom for the classical groups. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q)
Lie Groups and Lie Algebras: Lesson 31 - U(2,C) and GL(1,Q) In this lecture we back up and deploy the basis elements we eliminated in the su(2) and so(3) algebras when we enforced the determinants to be equal to 1. This expands the algebras to u(2) and o(3) and generates the groups U(2) a
From playlist Lie Groups and Lie Algebras
Chao Yang - Practical Quantum Circuits for Block Encodings of Sparse Matrices - IPAM at UCLA
Recorded 27 January 2022. Chao Yang of Lawrence Berkeley National Laboratory presents "Practical Quantum Circuits for Block Encodings of Sparse Matrices" at IPAM's Quantum Numerical Linear Algebra Workshop. Abstract: Many standard linear algebra problems can be solved on a quantum computer
From playlist Quantum Numerical Linear Algebra - Jan. 24 - 27, 2022
Stability, cohomology vanishing, and non-approximable groups - Andreas Thom
Stability and Testability Topic: Stability, cohomology vanishing, and non-approximable groups Speaker: Andreas Thom Affiliation: University of Dresden Date: December 2, 2020 For more video please visit http://video.ias.edu
From playlist Stability and Testability
Stanford Seminar - Highly optimized quantum circuits synthesized via data-flow engines
Peter Rakyta, Department of Physics of Complex Systems at Eötvös Loránd University November 9, 2022 The formulation of quantum programs in terms of the fewest number of gate operations is crucial to retrieve meaningful results from the noisy quantum processors accessible these days. In th
From playlist Stanford EE380-Colloquium on Computer Systems - Seminar Series
RT8.1. Schur Orthogonality Relations
Representation Theory of Finite Groups: As a first step to Fourier analysis on finite groups, we state and prove the Schur Orthogonality Relations. With these relations, we may form an orthonormal basis of matrix coefficients for L^(G), the set of functions on G. We also define charac
From playlist *** The Good Stuff ***
Lazaro Recht: Metric geometry in homogeneous spaces of the unitary group of a C* -algebra. 2
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Algebraic and Complex Geometry
Bachir Bekka - On characters of infinite groups
Let G be a countable infinite group. Unless G is virtually abelian, a description of the unitary dual of G (that is, the equivalence classes of irreducible unitary representations of G) is hopeless, as a consequence of theorems of Glimm and Thoma. A sensible substitute for the unitary dual
From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette
Tim Steger: Construction of lattices defining fake projective planes - lecture 3
Recording during the meeting "Ball Quotient Surfaces and Lattices " the February 26, 2019 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 Ma
From playlist Algebraic and Complex Geometry
Definition of a group Lesson 24
In this video we take our first look at the definition of a group. It is basically a set of elements and the operation defined on them. If this set of elements and the operation defined on them obey the properties of closure and associativity, and if one of the elements is the identity el
From playlist Abstract algebra
Operator Scaling via Geodesically Convex Optimization, Invariant Theory... - Yuanzhi Li
Computer Science/Discrete Mathematics Seminar I Topic: Operator Scaling via Geodesically Convex Optimization, Invariant Theory and Polynomial Identity Testing Speaker: Yuanzhi Li Affiliation: Princeton University Date: March 19, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics