In abstract algebra, a decomposition of a module is a way to write a module as a direct sum of modules. A type of a decomposition is often used to define or characterize modules: for example, a semisimple module is a module that has a decomposition into simple modules. Given a ring, the types of decomposition of modules over the ring can also be used to define or characterize the ring: a ring is semisimple if and only if every module over it is a semisimple module. An indecomposable module is a module that is not a direct sum of two nonzero submodules. Azumaya's theorem states that if a module has an decomposition into modules with local endomorphism rings, then all decompositions into indecomposable modules are equivalent to each other; a special case of this, especially in group theory, is known as the Krull–Schmidt theorem. A special case of a decomposition of a module is a decomposition of a ring: for example, a ring is semisimple if and only if it is a direct sum (in fact a product) of matrix rings over division rings (this observation is known as the Artin–Wedderburn theorem). (Wikipedia).
How to integrate by partial fractions
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook How to integrate by the method of partial fraction decomposition. In algebra, the partial fraction decomposition or partial fraction expansion of a rational fraction (that is a fraction such that the numerator
From playlist A second course in university calculus.
Ex: Setting Up Partial Fraction Decomposition
This video provides several examples of how to set up the fractions in order to perform partial fraction decomposition. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Performing Partial Fraction Decomposition
How to Set Up the Partial Fraction Decomposition
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Set Up the Partial Fraction Decomposition. Just setting them up. See my other videos for actual solved problems.
From playlist Partial Fraction Decomposition
Ex 2: Partial Fraction Decomposition (Linear Factors)
This video explains how to perform partial fraction decomposition when the denominator has 2 distinct linear factors. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Performing Partial Fraction Decomposition
Ex 1: Partial Fraction Decomposition (Linear Factors)
This video explains how to perform partial fraction decomposition when the denominator has 2 distinct linear factors. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Performing Partial Fraction Decomposition
Partial Fraction Decomposition Part 1 (Linear)
This video introduces partial fraction decomposition.
From playlist Integration Using Partial Fractions
Math 060 Linear Algebra 33 120514: Singular Value Decomposition 2/2
Singular Value Decomposition of a matrix: construction of the compact SVD; extending the matrices of the compact SVD to obtain the SVD.
From playlist Course 4: Linear Algebra
(New Version Available) Partial Fraction Decomposition - Part 1 of 2
New Version Available: https://youtu.be/c2oLHtPA03U This video explain how to perform partial fraction decomposition with linear factors. http://mathispower4u.yolasite.com/
From playlist Integration Using Partial Fraction Decomposition
Partial Fraction Decomposition - Part 2 of 2
This video explain how to perform partial fraction decomposition with linear and quadratic factors. http://mathispower4u.yolasite.com/
From playlist Integration Using Partial Fractions
Steve Oudot (9/8/21): Signed barcodes for multi-parameter persistence via rank decompositions
In this talk I will introduce the signed barcode, a new visual representation of the global structure of the rank invariant of a multi-parameter persistence module or, more generally, of a poset representation. Like its unsigned counterpart in one-parameter persistence, the signed barcode
From playlist AATRN 2021
Gregory Henselman-Petrusek (9/28/22): Saecular persistence
Homology with field coefficients has become a mainstay of modern TDA, thanks in part to structure theorems which decompose the corresponding persistence modules. This naturally begs the question -- what of integer coefficients? Or homotopy? We introduce saecular persistence, a categoric
From playlist AATRN 2022
Hecke Endomorphism Algebras, Stratification, finite groups of Lie type, and ı-quantum algebras
Recorded for UVa Conference Presented by Jie Du (joint work with B. Marshall and L. Scott)
From playlist Pure seminars
Francesco Vaccarino (8/29/21): Parallel decomposition of persistence modules through interval bases
We introduce an algorithm to decompose any finite-type persistence module with coefficients in a field into what we call an "interval basis". This construction yields both the standard persistence pairs of Topological Data Analysis (TDA), as well as a special set of generators inducing the
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Francesco Vaccarino (8/4/21): Parallel decomposition of persistence modules through interval bases
We introduce an algorithm to decompose any finite-type persistence module with coefficients in a field into what we call an "interval basis". This construction yields both the standard persistence pairs of Topological Data Analysis (TDA), as well as a special set of generators inducing the
From playlist AATRN 2021
Stability and Periodicity in Modular Representation Theory - Nate Harman
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Stability and Periodicity in Modular Representation Theory Speaker: Nate Harman Affiliation: Member, School of Mathematics Date: November 18, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Why do we care about characters of tilting modules? - Shotaro Makisumi
SL2 Seminar Topic: Why do we care about characters of tilting modules? Speaker: Shotaro Makisumi Affiliation: Columbia University; Member, School of Mathematics Date: January 26, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Yonatan harpaz : The universal property of topological Hochschild homology
CONFERENCE Recording during the thematic meeting : « Chromatic Homotopy, K-Theory and Functors» the January 24, 2023 at the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Jean Petit Find this video and other talks given by worldwide mathematicians on CIR
From playlist Topology
Geordie Williamson, Lecture VI - 30 January 2015
Geordie Williamson (Max-Planck-Institute, Bonn) - Lecture VI http://www.crm.sns.it/course/4033/ This mini-course will be an introduction to perverse sheaves, with emphasis on examples from representation theory. It will be a course full of pictures and examples, with the aim of trying to
From playlist Lie Theory and Representation Theory - 2015
Integration Using Partial Fraction Decomposition Part 1
This video shows how partial fraction decomposition can be used to simplify and integral. This video only shows linear factors. Part 1 of 2 Site: http://mathispower4u.com
From playlist Integration Using Partial Fractions
Broué’s Abelian Defect Group Conjecture I - Jay Taylor
Seminar on Geometric and Modular Representation Theory Topic: Broué’s Abelian Defect Group Conjecture I Speaker: Jay Taylor Affiliation: University of Southern California; Member, School of Mathematics Date: September 9, 2020 For more video please visit http://video.ias.edu
From playlist Seminar on Geometric and Modular Representation Theory