Matrix normal forms | Linear algebra
In linear algebra, the Hermite normal form is an analogue of reduced echelon form for matrices over the integers Z. Just as reduced echelon form can be used to solve problems about the solution to the linear system Ax=b where x is in Rn, the Hermite normal form can solve problems about the solution to the linear system Ax=b where this time x is restricted to have integer coordinates only. Other applications of the Hermite normal form include integer programming, cryptography, and abstract algebra. (Wikipedia).
Series solution of the Hermite differential equation. Shows how to construct the Hermite polynomials. Join me on Coursera: Differential equations for engineers https://www.coursera.org/learn/differential-equations-engineers Matrix algebra for engineers https://www.coursera.org/learn/matr
From playlist Differential Equations with YouTube Examples
Integral row reduction + Hermite normal form|Abstract Algebra Math Foundations 223 | NJ Wildberger
We have a careful look at getting a good basis of an integral linear space through a specific algorithm which is essentially that of Hermite normal form. Usually in linear algebra courses this is framed in terms of matrices, but here we are taking more of an mset point of view, but the ide
From playlist Math Foundations
Lattice relations + Hermite normal form|Abstract Algebra Math Foundations 224 | NJ Wildberger
We introduce lattices and integral linear spans of vexels. These are remarkably flexible, common and useful algebraic objects, and they are the direct integral analogs of vector spaces. To understand the structure of a given lattice, the algorithm to compute a Hermite normal form basis is
From playlist Math Foundations
We are – almost all of us – deeply attracted to the idea of being normal. But what if our idea of ‘normal’ isn’t normal? A plea for a broader definition of an important term. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/ojRR53 Join our mailing list: h
From playlist SELF
Math 060 Fall 2017 112717C Hermitian Matrices Part 1
Definitions: complex conjugate, modulus, complex vector, conjugate transpose, complex inner product, conjugate matrix. Hermitian matrices. Hermitian matrices and the inner product. Hermitian matrices have 1. real eigenvalues, 2. orthogonal eigenspaces. Unitary matrices. Hermitian matr
From playlist Course 4: Linear Algebra (Fall 2017)
Math 060 Fall 2017 120117 Normal Matrices; Preparation for Singular Value Decomposition
Recall definition of normal matrix, statement of Schur's theorem. Theorem: A is normal iff A is unitarily diagonalizable. Lemma: Any triangular normal matrix is diagonal. Preparatory material for singular value decomposition: the null space of A equals that of A^TA; and consequently the
From playlist Course 4: Linear Algebra (Fall 2017)
The Normal Distribution (1 of 3: Introductory definition)
More resources available at www.misterwootube.com
From playlist The Normal Distribution
A central limit theorem for Gaussian polynomials... pt1 -Anindya De
Anindya De Institute for Advanced Study; Member, School of Mathematics May 13, 2014 A central limit theorem for Gaussian polynomials and deterministic approximate counting for polynomial threshold functions In this talk, we will continue, the proof of the Central Limit theorem from my las
From playlist Mathematics
Under the Sea - With Helen Scales
A dive into the spiralling world of seashells and the bizarre animals that make them. Helen Scales explains how hermit crabs like to party and butterflies learnt to swim. Watch the Q&A: https://www.youtube.com/watch?v=GqBHjBDgLfY Subscribe for regular science videos: http://bit.ly/RiSubsc
From playlist Ri Talks
Linear Algebra 7.5 Hermitian, Unitary, and Normal Matrices
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.
From playlist Linear Algebra
Phong NGUYEN - Recent progress on lattices's computations 2
This is an introduction to the mysterious world of lattice algorithms, which have found many applications in computer science, notably in cryptography. We will explain how lattices are represented by computers. We will present the main hard computational problems on lattices: SVP, CVP and
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
8. Quantum Mechanical Harmonic Oscillator
MIT 5.61 Physical Chemistry, Fall 2017 Instructor: Professor Robert Field View the complete course: https://ocw.mit.edu/5-61F17 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62RsEHXe48Imi9-87FzQaJg This lecture covers the quantum mechanical treatment of the harmonic o
From playlist MIT 5.61 Physical Chemistry, Fall 2017
The Early Middle Ages, 284--1000 (HIST 210) Professor Freedman discusses some of the paradoxes of monasticism in the Early Middle Ages. To the modern mind, monks and learning make a natural pair. However, this combination is not an obvious outcome of early monasticism, which emphasized as
From playlist The Early Middle Ages, 284--1000 with Paul Freedman
Quantum Harmonic Oscillator Part 2
We solve the differential equation for the Quantum Harmonic Oscillator, using various "tricks" and Hermite Polynomials.
From playlist Quantum Mechanics Uploads
The Quantum Harmonic Oscillator Part 2: Solving the Schrödinger Equation
We just introduced the classical harmonic oscillator, so now let's look at the quantum version! Obviously this is much trickier, but let's solve the Schrödinger equation and see what the solution tells us about the quantum world. Script by Hèctor Mas Watch the whole Modern Physics playli
From playlist Modern Physics
10c Machine Learning: Polynomial Regression
Lecture on polynomial regression, including an intuitive alternative interpretation, basis expansion concepts and orthogonal basis through Hermite polynomials. Follow along with the demonstration workflow: https://github.com/GeostatsGuy/PythonNumericalDemos/blob/master/SubsurfaceDataAnaly
From playlist Machine Learning
In Which an Earthquake Convicts Seismologists of Manslaughter
**ORDER our new book: http://WeHaveNoIdea.com The AudioPH[i]D Ep. 2 - 12/4/12: In Which an Earthquake Convicts Seismologists of Manslaughter Laurence Yeung, Crystal Dilworth, Zach Tobin, and Evans Boney team up to bring us the most recent (well, sort of) academic news, a closer look at
From playlist The Audio Ph.[i]D. - News Podcast
Matrizen - normal, hermitesch, selbstadjungiert, unitär
Abonniert den Kanal oder unterstützt ihn auf Steady: https://steadyhq.com/en/brightsideofmaths Ihr werdet direkt informiert, wenn ich einen Livestream anbiete. Hier erkläre ich kurz die Bedeutung der transponierten Matrix und die Begriffe normal, selbstajdungiert, hermitesch und unitär.
From playlist Lineare Algebra