In operator theory, an area of mathematics, Douglas' lemma relates factorization, range inclusion, and majorization of Hilbert space operators. It is generally attributed to Ronald G. Douglas, although Douglas acknowledges that aspects of the result may already have been known. The statement of the result is as follows: Theorem: If and are bounded operators on a Hilbert space , the following are equivalent: 1. * 2. * for some 3. * There exists a bounded operator on such that . Moreover, if these equivalent conditions hold, then there is a unique operator such that * * * . A generalization of Douglas' lemma for unbounded operators on a Banach space was proved by Forough (2014). (Wikipedia).
Linear Algebra Vignette 2a: RREF - What It's For
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Linear Algebra Vignette 2d: RREF And The Inverse Matrix
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Linear Algebra Vignette 3d: Easy Eigenvalues - Linearly Dependent Columns
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Problems, Paradoxes, and Sophisms
Suvrit Sra: Lecture series on Aspects of Convex, Nonconvex, and Geometric Optimization (Lecture 2)
The lecture was held within the framework of the Hausdorff Trimester Program "Mathematics of Signal Processing". (26.1.2016)
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
Linear Algebra Vignette 1a: Matrix Representation of a Linear Transformation
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Linear Algebra Vignette 3a: Easy Eigenvalues - Introduction
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Yi Wang: The Helton-Howe trace formula on submodules
Talk by Yi Wang in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar.html on August 19, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
Ulrich Bauer (4/6/22): Persistence in functional topology
I will illustrate the central role and the historical development of persistent homology beyond applied topology, connecting recent developments in persistence theory with classical results in critical point theory and the calculus of variations. Presenting recent joint work with M. Schmah
From playlist AATRN 2022
David McAllester - Dependent Type Theory from the Perspective of Mathematics, Physics, and (...)
Dependent type theory imposes a type system on Zemelo-Fraenkel set theory (ZFC). From a mathematics and physics perspective dependent type theory naturally generalizes the Bourbaki notion of structure and provides a universal notion of isomorphism and symmetry. This comes with a universal
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Patrick Massot - Why Explain Mathematics to Computers?
A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk, I'll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be us
From playlist Mikefest: A conference in honor of Michael Douglas' 60th birthday
Camillo De Lellis - Tribute to Ennio De Giorgi - 20 September 2016
De Lellis, Camillo "Min-max methods for surfaces with boundary"
From playlist A Mathematical Tribute to Ennio De Giorgi
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Problems, Paradoxes, and Sophisms
Linear Algebra Vignette 3h: Easy Eigenvalues - The Grand Finale
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Gromov–Witten Invariants and the Virasoro Conjecture (Remote Talk) by Ezra Getzler
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
Planarity in Higher Codimension Mean Curvature Flow - Keaton Naff
Analysis Seminar Topic: Planarity in Higher Codimension Mean Curvature Flow Speaker: Keaton Naff Affiliation: Columbia University Date: February 08, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
Linear Algebra Vignette 3c: Easy Eigenvalues - Sums Of Rows
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Linear Algebra Vignette 3e: Easy Eigenvalues - Triangular Matrices
This course is on Lemma: http://lem.ma Lemma looking for developers: http://lem.ma/jobs Other than http://lem.ma, I recommend Strang http://bit.ly/StrangYT, Gelfand http://bit.ly/GelfandYT, and my short book of essays http://bit.ly/HALAYT Questions and comments below will be prompt
From playlist Linear Algebra Vignettes
Frank Morgan: Soap Bubbles and Mathematics
Summary: Soap bubbles, with applications from cappuccino to universes, illustrate some fundamental questions in mathematics. The show will include some demonstrations. Frank Morgan is an American mathematician and the Webster Atwell '21 Professor of Mathematics at Williams College, specia
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