Mathematical constants | Geometry of numbers | Systolic geometry

Hermite constant

In mathematics, the Hermite constant, named after Charles Hermite, determines how short an element of a lattice in Euclidean space can be. The constant γn for integers n > 0 is defined as follows. For a lattice L in Euclidean space Rn with unit covolume, i.e. vol(Rn/L) = 1, let λ1(L) denote the least length of a nonzero element of L. Then √γn is the maximum of λ1(L) over all such lattices L. The square root in the definition of the Hermite constant is a matter of historical convention. Alternatively, the Hermite constant γn can be defined as the square of the maximal systole of a flat n-dimensional torus of unit volume. (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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Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a Hermite polynomial. Previous videos showed the solution best describe the quantum oscillator of the Schrodinger equation is the product of a constant that needed to be normalized, mu

From playlist THE "WHAT IS" PLAYLIST

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Visit http://ilectureonline.com for more math and science lectures! In this video I will calculate the first few Hermitian polynomials stating with n=0 to n=3. Next video in this series can be seen at: https://youtu.be/9euxAKJDll0

From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION

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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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I define one of the most important constants in mathematics, the Euler-Mascheroni constant. It intuitively measures how far off the harmonic series 1 + 1/2 + ... + 1/n is from ln(n). In this video, I show that the constant must exist. It is an open problem to figure out if the constant is

From playlist Series

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Hermitian Operators (Self-Adjoint Operators) | Quantum Mechanics

In this video, we will talk about Hermitian operators in quantum mechanics. If an operator A is a Hermitian operator, then it is the same as its adjoint operator A-dagger, which is defined via this equation here. Usually, the terms "Hermitian" and "self adjoint" are used interchangeably, h

From playlist Quantum Mechanics, Quantum Field Theory

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From playlist Course 4: Linear Algebra (Fall 2017)

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From playlist Write Linear Equations

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From playlist NPTEL: Elementary Numerical Analysis | CosmoLearning Mathematics

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From playlist Machine Learning

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From playlist PHYSICS 66.1 QUANTUM MECHANICS - SCHRODINGER EQUATION

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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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From playlist Zill DE 4.1 Preliminary Theory - Linear Equations

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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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PROGRAM: TOPICS IN HIGH DIMENSIONAL PROBABILITY ORGANIZERS: Anirban Basak (ICTS-TIFR, India) and Riddhipratim Basu (ICTS-TIFR, India) DATE & TIME: 02 January 2023 to 13 January 2023 VENUE: Ramanujan Lecture Hall This program will focus on several interconnected themes in modern probab

From playlist TOPICS IN HIGH DIMENSIONAL PROBABILITY

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Overview of Linear equations - Free Math Videos - Online Tutor

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From playlist Number Theory Research Unit at CAMS - AUB

Related pages

Gamma function | Charles Hermite | Mathematics | Square root | Lattice (group) | Euclidean space | Hexagonal lattice | Torus | Loewner's torus inequality | Systolic geometry