Homogeneous polynomials | Diophantine equations | Field (mathematics)
In mathematics, a norm form is a homogeneous form in n variables constructed from the field norm of a field extension L/K of degree n. That is, writing N for the norm mapping to K, and selecting a basis e1, ..., en for L as a vector space over K, the form is given by N(x1e1 + ... + xnen) in variables x1, ..., xn. In number theory norm forms are studied as Diophantine equations, where they generalize, for example, the Pell equation. For this application the field K is usually the rational number field, the field L is an algebraic number field, and the basis is taken of some order in the ring of integers OL of L. (Wikipedia).
From playlist Linear Algebra Ch 6
From playlist Linear Algebra Ch 6
Wen Shen, Penn State University. Lectures are based on my book: "An Introduction to Numerical Computation", published by World Scientific, 2016. See promo video: https://youtu.be/MgS33HcgA_I
From playlist CMPSC/MATH 451 Videos. Wen Shen, Penn State University
Example of Rational Canonical Form 3
Matrix Theory: We note two formulations of Rational Canonical Form. A recipe is given for combining and decomposing companion matrices using cyclic vectors.
From playlist Matrix Theory
Matrix Norms : Data Science Basics
What does it mean to take the norm of a matrix? Vector Norms Video: https://www.youtube.com/watch?v=5fN2J8wYnfw Eigenvalues and Eigenvectors Video: https://www.youtube.com/watch?v=glaiP222JWA
From playlist Data Science Basics
13C Norm and Distance in Euclidean n Space
Norm and distance in Euclidean n-Space.
From playlist Linear Algebra
Example of Rational Canonical Form 2: Several Blocks
Matrix Theory: Let A be a 12x12 real matrix with characteristic polynomial (x^2+1)^6, minimal polynomial (x^2 + 1)^3, and dim(Null(A^2 + I)) = 6. Find all possible rational canonical forms for A.
From playlist Matrix Theory
Nathan Dunfield, Lecture 2: A Tale of Two Norms
33rd Workshop in Geometric Topology, Colorado College, June 10, 2016
From playlist Nathan Dunfield: 33rd Workshop in Geometric Topology
Topology of Norms Defined by Systems of Linear forms - Pooya Hatami
Pooya Hatami University of Chicago May 7, 2012 Gowers' uniformity norms are defined by average of a function over specific sets of linear forms. We study norms that are similarly defined by a system of linear forms. We prove that for bounded complex functions over FnpFpn, each such norm is
From playlist Mathematics
A Spirit of Trust: Magnanimity and Agency in Hegel’s Phenomenology
Robert Brandom is Distinguished Professor of Philosophy and Fellow at the Center for Philosophy of Science at the University of Pittsburgh. He is the author of thirteen books, including Making It Explicit: Reasoning, Representing, and Discursive Commitment. His most recent book, A Spirit o
From playlist Franke Lectures in the Humanities
Testing Correlations and Inverse Theorems - Hamed Hatami
Hamed Hatami Institute for Advanced Study/Princeton University February 23, 2010 The uniformity norms are defined in different contexts in order to distinguish the ``typical'' random functions, from the functions that contain certain structures. A typical random function has small uniform
From playlist Mathematics
Lecture 16 | Introduction to Linear Dynamical Systems
Professor Stephen Boyd, of the Electrical Engineering department at Stanford University, lectures on the use of symmetric matrices, quadratic forms, matrix norm, and SVDs in LDS for the course Introduction to Linear Dynamical Systems (EE263). Introduction to applied linear algebra and l
From playlist Lecture Collection | Linear Dynamical Systems
The symplectic displacement energy - Peter Spaeth
Peter Spaeth GE Global Research February 20, 2015 To begin we will recall Banyaga's Hofer-like metric on the group of symplectic diffeomorphisms, and explain its conjugation invariance up to a factor. From there we will prove the positivity of the symplectic displacement energy of open su
From playlist Mathematics
Hilbert Space Techniques in Complex Analysis and Geometry (Lecture 5) by Dror Varolin
PROGRAM CAUCHY-RIEMANN EQUATIONS IN HIGHER DIMENSIONS ORGANIZERS: Sivaguru, Diganta Borah and Debraj Chakrabarti DATE: 15 July 2019 to 02 August 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Complex analysis is one of the central areas of modern mathematics, and deals with holomo
From playlist Cauchy-Riemann Equations in Higher Dimensions 2019
Interpreting Polynomial Structure Analytically - Julia Wolf
Julia Wolf Rutgers, The State University of New Jersey February 8, 2010 I will be describing recent joint efforts with Tim Gowers to decompose a bounded function into a sum of polynomially structured phases and a uniform error, based on the recent inverse theorem for the Uk norms on Fpn b
From playlist Mathematics
Counting points on the E8 lattice with modular forms (theta functions) | #SoME2
In this video, I show a use of modular forms to answer a question about the E8 lattice. This video is meant to serve as an introduction to theta functions of lattices and to modular forms for those with some knowledge of vector spaces and series. -------------- References: (Paper on MIT
From playlist Summer of Math Exposition 2 videos
Norm Form Equations and Linear Divisibility Sequences (CTNT 2020)
Contact Information: Elisa Bellah ebellah@uoregon.edu pages.uoregon.edu/ebellah Abstract: Finding integer solutions to norm form equations is a classic Diophantine problem. Using the units of the associated coefficient ring, we can produce sequences of solutions to these equations. It tur
From playlist CTNT 2020 - Conference Videos
Stanford ENGR108: Introduction to Applied Linear Algebra | 2020 | Lecture 9 - VMLS norm
Professor Stephen Boyd Samsung Professor in the School of Engineering Director of the Information Systems Laboratory To follow along with the course schedule and syllabus, visit: https://web.stanford.edu/class/engr108/ To view all online courses and programs offered by Stanford, visit:
From playlist Stanford ENGR108: Introduction to Applied Linear Algebra —Vectors, Matrices, and Least Squares