Homogeneous polynomials | Diophantine equations | Field (mathematics)

Norm form

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).

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ch6 3. Matrix norms. Wen Shen

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

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11D The Norm of a Vector

The norm or length of a vector.

From playlist Linear Algebra

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11C The Norm of a Vector

The normal or length of a vector.

From playlist Linear Algebra

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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

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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

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13C Norm and Distance in Euclidean n Space

Norm and distance in Euclidean n-Space.

From playlist Linear Algebra

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

Related pages

Field extension | Algebraic number field | Diophantine equation | Mathematics | Field norm | Order (ring theory) | Ring of integers | Number theory