Matrix normal forms | Linear algebra

Hermite normal form

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).

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Hermite differential equation

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

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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

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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

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How Can I Be More Normal?

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From playlist SELF

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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)

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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)

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The Normal Distribution (1 of 3: Introductory definition)

More resources available at www.misterwootube.com

From playlist The Normal Distribution

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A central limit theorem for Gaussian polynomials... pt1 -Anindya De

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From playlist Mathematics

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Under the Sea - With Helen Scales

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From playlist Ri Talks

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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

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Phong NGUYEN - Recent progress on lattices's computations 2

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From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory

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8. Quantum Mechanical Harmonic Oscillator

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From playlist MIT 5.61 Physical Chemistry, Fall 2017

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13. Monasticism

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From playlist The Early Middle Ages, 284--1000 with Paul Freedman

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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

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The Quantum Harmonic Oscillator Part 2: Solving the Schrödinger Equation

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From playlist Modern Physics

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10c Machine Learning: Polynomial Regression

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From playlist Machine Learning

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From playlist The Audio Ph.[i]D. - News Podcast

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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

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Number Theory Library | MATLAB | Linear algebra | Lattice (group) | PARI/GP | Howell normal form | Smith normal form | Principal ideal domain | Determinant | Gaussian elimination | Unimodular matrix | Integer programming | Cryptography | Dedekind domain | Control theory | Hermite ring | Maple (software) | Integer | Wolfram Mathematica | Lenstra–Lenstra–Lovász lattice basis reduction algorithm | SageMath | Diophantine equation | Abstract algebra | Pivot element | Matrix (mathematics) | Invertible matrix