Unsolved problems in mathematics | Combinatorial design | Matrices

Hadamard matrix

In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose rows are mutually orthogonal. In geometric terms, this means that each pair of rows in a Hadamard matrix represents two perpendicular vectors, while in combinatorial terms, it means that each pair of rows has matching entries in exactly half of their columns and mismatched entries in the remaining columns. It is a consequence of this definition that the corresponding properties hold for columns as well as rows. The n-dimensional parallelotope spanned by the rows of an n×n Hadamard matrix has the maximum possible n-dimensional volume among parallelotopes spanned by vectors whose entries are bounded in absolute value by 1. Equivalently, a Hadamard matrix has maximal determinant among matrices with entries of absolute value less than or equal to 1 and so is an extremal solution of Hadamard's maximal determinant problem. Certain Hadamard matrices can almost directly be used as an error-correcting code using a Hadamard code (generalized in Reed–Muller codes), and are also used in balanced repeated replication (BRR), used by statisticians to estimate the variance of a parameter estimator. (Wikipedia).

Video thumbnail

What is the "hadron" in the name Large Hadron Collider?

Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu

From playlist Science Unplugged: Particle Physics

Video thumbnail

Le "Large Hadron Collider" (français)

un apreçu du grand collisionneur de hadrons (LHC) et de son programme de recherche

From playlist Français

Video thumbnail

Linear Algebra for Computer Scientists. 12. Introducing the Matrix

This computer science video is one of a series of lessons about linear algebra for computer scientists. This video introduces the concept of a matrix. A matrix is a rectangular or square, two dimensional array of numbers, symbols, or expressions. A matrix is also classed a second order

From playlist Linear Algebra for Computer Scientists

Video thumbnail

What is a Matrix?

What is a matrix? Free ebook http://tinyurl.com/EngMathYT

From playlist Intro to Matrices

Video thumbnail

The Large Hadron Collider

A 10' overview of the LHC project and its research plans

From playlist The Large Hadron Collider

Video thumbnail

2 Construction of a Matrix-YouTube sharing.mov

This video shows you how a matrix is constructed from a set of linear equations. It helps you understand where the various elements in a matrix comes from.

From playlist Linear Algebra

Video thumbnail

Complex Matrices ( An intuitive visualization )

Complex Matrices are not given enough credit for what they do and even when they are used its often introduced as an foreign entity. This video was made to shed light on such a misinterpreted topic. Timestamps 00:00 - Introduction 00:11 - Matrix 00:45 - Complex Number 02:50 - Complex Ma

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Column space of a matrix

We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the

From playlist Introducing linear algebra

Video thumbnail

il Large Hadron Collider (Italiano)

Una panoramica sul progetto LHC ed i suoi campi di ricerca.

From playlist Italiano

Video thumbnail

Basic Tensor Arithmetic (The Hadamard Product) — Topic 12 of Machine Learning Foundations

In this video from my Machine Learning Foundations series, I demonstrate basic tensor arithmetic (including the Hadamard product) through hands-on code demos in NumPy, TensorFlow, and PyTorch. There are eight subjects covered comprehensively in the ML Foundations series and this video is

From playlist Linear Algebra for Machine Learning

Video thumbnail

Topics in Combinatorics lecture 5.0 --- Sets of vectors with no acute angles, and Hadamard matrices

How many vectors can you find in R^n if the angle between any two of them is at least a right angle? It's easy to see that one can find 2n such vectors, but can one do any better than this? And what if the vectors have to have all coordinates equal to 1 or -1? This video contains answers t

From playlist Topics in Combinatorics (Cambridge Part III course)

Video thumbnail

Lec 20 | MIT 6.451 Principles of Digital Communication II, Spring 2005

The Sum-Product Algorithm View the complete course: http://ocw.mit.edu/6-451S05 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.451 Principles of Digital Communication II

Video thumbnail

DDPS | Entropy stable schemes for nonlinear conservation laws

High order methods are known to be unstable when applied to nonlinear conservation laws with shocks and turbulence, and traditionally require additional filtering, limiting, or artificial viscosity to avoid solution blow up. Entropy stable schemes address this instability by ensuring that

From playlist Data-driven Physical Simulations (DDPS) Seminar Series

Video thumbnail

From Classical to Quantum Stochastic Process by Soham Biswas

DISCUSSION MEETING STATISTICAL PHYSICS: RECENT ADVANCES AND FUTURE DIRECTIONS (ONLINE) ORGANIZERS: Sakuntala Chatterjee (SNBNCBS, Kolkata), Kavita Jain (JNCASR, Bangalore) and Tridib Sadhu (TIFR, Mumbai) DATE: 14 February 2022 to 15 February 2022 VENUE: Online In the past few dec

From playlist Statistical Physics: Recent advances and Future directions (ONLINE) 2022

Video thumbnail

Basis and Quantum State; Quantum Operators

In this video, we review concepts of quantum basis and quantum state (in a finite-dimensional Hilbert space) and how to implement them in the Wolfram Quantum Framework. We also discuss the basis transformation. For more info and examples, please visit the Wolfram Quantum Framework resource

From playlist Daily Study Group: Quantum Computation Framework

Video thumbnail

Thomas Stoll: On generalised Rudin-Shapiro sequences

CIRM VIRTUAL CONFERENCE Recorded during the meeting "​ Diophantine Problems, Determinism and Randomness" the November 26, 2020 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide

From playlist Virtual Conference

Video thumbnail

Introducing Hadamard Binary Neural Networks

To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Yash Akhauri Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and

From playlist Wolfram Technology Conference 2018

Video thumbnail

Quantum computation (Lecture 02) by Peter Young

ORGANIZERS : Abhishek Dhar and Sanjib Sabhapandit DATE : 27 June 2018 to 13 July 2018 VENUE : Ramanujan Lecture Hall, ICTS Bangalore This advanced level school is the ninth in the series. This is a pedagogical school, aimed at bridging the gap between masters-level courses and topics

From playlist Bangalore School on Statistical Physics - IX (2018)

Video thumbnail

Christian Bär: Local index theory for Lorentzian manifolds

HYBRID EVENT We prove a local version of the index theorem for Dirac-type operators on globally hyperbolic Lorentzian manifolds with Cauchy boundary. In case the Cauchy hypersurface is compact, we do not assume self-adjointness of the Dirac operator on the spacetime or of the associated el

From playlist Mathematical Physics

Video thumbnail

What's left to do at the Large Hadron Collider?

The second run, or second season, begins at CERN's Large Hadron Collider. Can it top season one's discovery of the Higgs Boson!? See our videos from inside the LHC: http://bit.ly/LHCvideos This video features Professor Ed Copeland. See Ed's trilogy of extended interviews: http://bit.ly/C

From playlist Large Hadron Collider - Sixty Symbols

Related pages

Graphs and Combinatorics | Perpendicular | Complex Hadamard matrix | Absolute value | Vector space | Finite field | Raymond Paley | James Joseph Sylvester | Trace (linear algebra) | Weighing matrix | Balanced repeated replication | Quincunx matrix | Volume | Estimator | Solomon W. Golomb | Hadamard's inequality | Identity matrix | Parameter | Compressed sensing | Hadamard's maximal determinant problem | Congruence relation | Linear code | Paley construction | Combinatorics | Conjugate transpose | Determinant | Plackett–Burman design | Hadamard code | Walsh matrix | Variance | Sign (mathematics) | Combinatorial design | Mathematics | Reed–Muller code | Square matrix | Parallelepiped | Symmetric matrix | Quantum logic gate | Prime number | John Williamson (mathematician) | Equivalence relation | Kronecker product | Orthogonal matrix | Walsh function | Group homomorphism | Transpose | Tournament (graph theory) | Jacques Hadamard | Hadamard transform | Quantum computing