Linear algebra | Invariant subspaces
In mathematics, a linear operator T on a vector space is semisimple if every T-invariant subspace has a complementary T-invariant subspace; in other words, the vector space is a semisimple representation of the operator T. Equivalently, a linear operator is semisimple if the minimal polynomial of it is a product of distinct irreducible polynomials. A linear operator on a finite dimensional vector space over an algebraically closed field is semisimple if and only if it is diagonalizable. Over a perfect field, the Jordan–Chevalley decomposition expresses an endomorphism as a sum of a semisimple endomorphism s and a nilpotent endomorphism n such that both s and n are polynomials in x. (Wikipedia).
Math: Partial Differential Eqn. - Ch.1: Introduction (4 of 42) Partial Differential Operator
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the partial differential operator and how, again like the previous video, different notations are used to express the same thing. Yes! I'm convinced mathematicians invent different no
From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION
Cristina Câmara: Truncated Toeplitz operators
Abstract: Toeplitz matrices and operators constitute one of the most important and widely studied classes of non-self-adjoint operators. In this talk we consider truncated Toeplitz operators, a natural generalisation of finite Toeplitz matrices. They appear in various contexts, such as the
From playlist Analysis and its Applications
Schemes 46: Differential operators
This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we define differential operators on rings, and calculate the universal (normalized) differential operator of order n. As a special case we fin
From playlist Algebraic geometry II: Schemes
Dimitry Gurevich - q-cut-and-join Operators and q-Capelli Identity on Reflection Equation Algebras
There exists a way, based on the notion of Quantum Doubles, to introduce analogs of partial derivatives on the so-called Reflection Equation algebras. Analogously to the classical case it is possible to use these ”q-derivatives” for different applications. I plan to explain their utility f
From playlist Combinatorics and Arithmetic for Physics: special days
Representations of finite groups of Lie type (Lecture - 3) by Dipendra Prasad
PROGRAM GROUP ALGEBRAS, REPRESENTATIONS AND COMPUTATION ORGANIZERS: Gurmeet Kaur Bakshi, Manoj Kumar and Pooja Singla DATE: 14 October 2019 to 23 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Determining explicit algebraic structures of semisimple group algebras is a fund
From playlist Group Algebras, Representations And Computation
TQFTs from non-semisimple modular categories and modified traces, Marco de Renzi, Lecture II
Lecture series on modified traces in algebra and topology Topological Quantum Field Theories (TQFTs for short) provide very sophisticated tools for the study of topology in dimension 2 and 3: they contain invariants of 3-manifolds that can be computed by cut-and-paste methods, and their e
From playlist Lecture series on modified traces in algebra and topology
TQFTs from non-semisimple modular categories and modified traces, Marco de Renzi, Lecture III
Lecture series on modified traces in algebra and topology Topological Quantum Field Theories (TQFTs for short) provide very sophisticated tools for the study of topology in dimension 2 and 3: they contain invariants of 3-manifolds that can be computed by cut-and-paste methods, and their e
From playlist Lecture series on modified traces in algebra and topology
Partial Derivatives and the Gradient of a Function
We've introduced the differential operator before, during a few of our calculus lessons. But now we will be using this operator more and more over the prime symbol we are used to when describing differentiation, as from now on we will frequently be differentiating with respect to a specifi
From playlist Mathematics (All Of It)
Partial derivatives of vector fields
How do you intepret the partial derivatives of the function which defines a vector field?
From playlist Multivariable calculus
15 Properties of partially ordered sets
When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.
From playlist Abstract algebra
Paolo Piazza: Proper actions of Lie groups and numeric invariants of Dirac operators
HYBRID EVENT shall explain how to define and investigate primary and secondary invariants of G-invariant Dirac operators on a cocompact G-proper manifold, with G a connected real reductive Lie group. This involves cyclic cohomology and Ktheory. After treating the case of cyclic cocycles a
From playlist Lie Theory and Generalizations
Representation theory and geometry – Geordie Williamson – ICM2018
Plenary Lecture 17 Representation theory and geometry Geordie Williamson Abstract: One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theor
From playlist Plenary Lectures
"Introduction to p-adic harmonic analysis" James Arthur, University of Toronto [2008]
James Arthur, University of Toronto Introduction to harmonic analysis on p-adic groups Tuesday Aug 12, 2008 11:00 - 12:00 The stable trace formula, automorphic forms, and Galois representations Video taken from: http://www.birs.ca/events/2008/summer-schools/08ss045/videos/watch/200808121
From playlist Mathematics
Yves Benoist - Random walk on p-adic flag varieties
Yves Benoist (Université Paris Sud, France) According to a theorem of Furstenberg, a Zariski dense probability measure on a real semisimple Lie group admits a unique stationary probability measure on the flag variety. In this talk we will see that a Zariski dense probability measure on a
From playlist T1-2014 : Random walks and asymptopic geometry of groups.
Semirings that are finite and have infinity
Semirings. You can find the simple python script here: https://gist.github.com/Nikolaj-K/f036fd07991fce26274b5b6f15a6c032 Previous video: https://youtu.be/ws6vCT7ExTY
From playlist Algebra
Multivariable Calculus | Definition of partial derivatives.
We give the definition of the partial derivative of a function of more than one variable. In addition, we present some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Multivariable Calculus
Anton Alekseev: Poisson-Lie duality and Langlands duality via Bohr-Sommerfeld
Abstract: Let G be a connected semisimple Lie group with Lie algebra 𝔤. There are two natural duality constructions that assign to it the Langlands dual group G^∨ (associated to the dual root system) and the Poisson-Lie dual group G^∗. Cartan subalgebras of 𝔤^∨ and 𝔤^∗ are isomorphic to ea
From playlist Topology
Peter Scholze - 5/6 On the local Langlands conjectures for reductive groups over p-adic fields
Hadamard Lectures 2017 Abstract: Consider a reductive group G over a p-adic field F. The local Langlands conjecture relates the irreducible smooth representations of G(F) with the set of (local) L-parameters, which are maps from the Weil group of F to the L-group of G; refinements of the
From playlist Hadamard Lectures 2017 - Peter Scholze - On the local Langlands conjectures for reductive groups over p-adic fields
Peter Scholze - 6/6 On the local Langlands conjectures for reductive groups over p-adic fields
Hadamard Lectures 2017 Abstract: Consider a reductive group G over a p-adic field F. The local Langlands conjecture relates the irreducible smooth representations of G(F) with the set of (local) L-parameters, which are maps from the Weil group of F to the L-group of G; refinements of the
From playlist Hadamard Lectures 2017 - Peter Scholze - On the local Langlands conjectures for reductive groups over p-adic fields
Partial Implicit Differentiation
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From playlist Functions of Several Variables - Calculus