Linear algebra | Signal processing
In linear algebra, the restricted isometry property (RIP) characterizes matrices which are nearly orthonormal, at least when operating on sparse vectors. The concept was introduced by Emmanuel Candès and Terence Tao and is used to prove many theorems in the field of compressed sensing. There are no known large matrices with bounded restricted isometry constants (computing these constants is strongly NP-hard, and is hard to approximate as well), but many random matrices have been shown to remain bounded. In particular, it has been shown that with exponentially high probability, random Gaussian, Bernoulli, and partial Fourier matrices satisfy the RIP with number of measurements nearly linear in the sparsity level. The current smallest upper bounds for any large rectangular matrices are for those of Gaussian matrices. Web forms to evaluate bounds for the Gaussian ensemble are available at the Edinburgh Compressed Sensing RIC page. (Wikipedia).
Joe Neeman: Gaussian isoperimetry and related topics II
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Properties of Isosceles Triangles (Proof) - Geometry
http://www.youtube.com/vinteachesmath This video focuses on proving that the base angles in an isosceles triangle are congruent. In this properties of isosceles triangles proof, the follow concepts are covered: triangle altitude, the reflexive property and the hypotenuse leg condition fo
From playlist Geometry
Joe Neeman: Gaussian isoperimetry and related topics I
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
Isosceles & Equilateral Triangle Properties
I introduce 2 theorems about the properties of Isosceles and Equilateral Triangles. These theorems discuss how the base angles are congruent and that the bisector of the vertex is also a perpendicular bisector of the base. This video includes 2 proofs and 2 algebraic examples. EXAMPLES
From playlist Geometry
Joe Neeman: Gaussian isoperimetry and related topics III
The Gaussian isoperimetric inequality gives a sharp lower bound on the Gaussian surface area of any set in terms of its Gaussian measure. Its dimension-independent nature makes it a powerful tool for proving concentration inequalities in high dimensions. We will explore several consequence
From playlist Winter School on the Interplay between High-Dimensional Geometry and Probability
The isosceles triangle theorem is actually really simple! (KristaKingMath)
► My Geometry course: https://www.kristakingmath.com/geometry-course In this video we'll learn about the isosceles triangle theorem, which tells us that, when we have an isosceles triangle (a triangle in which two of the sides are congruent), the angles opposite the congruent sides will a
From playlist Geometry
Isotonic regression in general dimensions – Richard Samworth, University of Cambridge
Many problems in science and engineering involve an underlying unknown complex process that depends on a large number of parameters. The goal in many applications is to reconstruct, or learn, the unknown process given some direct or indirect observations. Mathematically, such a problem can
From playlist Approximating high dimensional functions
This geometry video tutorial provides a basic introduction into isosceles trapezoids. It discusses the basic properties of isosceles trapezoids. The bases are parallel and the legs are congruent. The lower base angles are congruent and the upper base angles are congruent. The lower bas
From playlist Geometry Video Playlist
Felix Krahmer: The Restricted Isometry Property for Random Gabor Synthesis Matrices
Felix Krahmer: The Restricted Isometry Property for Random Gabor Synthesis Matrices Abstract: The theory of compressed sensing considers the following problem: Let A be an m x n matrix and let x be s-sparse, i.e., all but s of its entries vanish. One seeks to recover x uniquely and effici
From playlist HIM Lectures: Trimester Program "Mathematics of Signal Processing"
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
Lie Groups and Lie Algebras: Lesson 10: The Classical Groups part VIII
Lie Groups and Lie Algebras: Lesson 10: The Classical Groups part VIII In this lecture we demonstrate the canonical form of a bilinear symmetric metric. This will help us appreciate that all of the most important types of metrics can be represented by matrices of a specific "canonical" ty
From playlist Lie Groups and Lie Algebras
Lipschitz rigidity for scalar curvature - Bernhard Hanke
Analysis & Mathematical Physics Topic: Lipschitz rigidity for scalar curvature Speaker: Bernhard Hanke Affiliation: University of Augsburg, Member, School of Mathematics Date: October 05, 2022 Lower scalar curvature bounds on spin Riemannian manifolds exhibit remarkable rigidity properti
From playlist Mathematics
Ahlfors Bers 2014 "The complex geometry of Teichmüller space and symmetric domains"
Stergios Antonakoudis (Cambridge University): From a complex analytic perspective, Teichmüller spaces can be realized as contractible bounded domains in complex vector spaces by the Bers embeddings. Bounded Symmetric domains constitute another class of bounded domains that has been extensi
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
Emily Stark: Action rigidity for free products of hyperbolic manifold groups
CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 22, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Virtual Conference
Atomistically inspired origami
Oxford Mathematics Public Lectures - Richard James - Atomistically inspired origami The World population is growing at about 80 million per year. As time goes by, there is necessarily less space per person. Perhaps this is why the scientific community seems to be obsessed with folding t
From playlist Oxford Mathematics Public Lectures
Nadia Larsen: Equilibrium states for C*-algebras of right LCM monoids.
Talk by Nadia Larsen in Global Noncommutative Geometry Seminar (Europe) http://www.noncommutativegeometry.nl/ncgseminar/ on October 13, 2020.
From playlist Global Noncommutative Geometry Seminar (Europe)
Proper Actions and Representation Theory Part 1
Professor Toshiyuki Kobayashi, University of Tokyo, Japan
From playlist Distinguished Visitors Lecture Series
What are some characteristics of an isosceles trapezoid
👉 Learn how to solve problems with trapezoids. A trapezoid is a four-sided shape (quadrilateral) such that one pair of opposite sides are parallel. Some of the properties of trapezoids are: one pair of opposite sides are parallel, etc. A trapezoid is isosceles is one pair of opposite sides
From playlist Properties of Trapezoids
Structured Regularization Summer School - A.Hansen - 1/4 - 19/06/2017
Anders Hansen (Cambridge) Lectures 1 and 2: Compressed Sensing: Structure and Imaging Abstract: The above heading is the title of a new book to be published by Cambridge University Press. In these lectures I will cover some of the main issues discussed in this monograph/textbook. In par
From playlist Structured Regularization Summer School - 19-22/06/2017