A complex Hadamard matrix is any complex matrix satisfying two conditions: * unimodularity (the modulus of each entry is unity): * orthogonality: , where denotes the Hermitian transpose of and is the identity matrix. The concept is a generalization of the Hadamard matrix. Note that any complex Hadamard matrix can be made into a unitary matrix by multiplying it by ; conversely, any unitary matrix whose entries all have modulus becomes a complex Hadamard upon multiplication by . Complex Hadamard matrices arise in the study of operator algebras and the theory of quantum computation. Real Hadamard matrices and Butson-type Hadamard matrices form particular cases of complex Hadamard matrices. Complex Hadamard matrices exist for any natural (compare the real case, in which existence is not known for every ). For instance the Fourier matrices (the complex conjugate of the DFT matrices without the normalizing factor), belong to this class. (Wikipedia).
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
ComplexMultiplication 1/3 - i/3
From playlist Complex Multiplication
From playlist Complex Multiplication
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
In this video, we'll learn how to view a complex number as a 2x2 matrix with a special form. We'll also see that there is a matrix version for the number 1 and a matrix representation for the imaginary unit, i. Furthermore, the matrix representation for i has the defining feature of the im
From playlist Complex Numbers
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
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
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
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
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
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)
Review, Quantum Circuits and Algorithms (Collection of Simple Gates)
In this video, we review our multi-part discussion of the Wolfram Quantum Framework and discuss how it works, how to define relevant objects (such as a quantum circuit) and how to implement different quantum algorithms. For more info and examples, please visit the Wolfram Quantum Framework
From playlist Daily Study Group: Quantum Computation Framework
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
Finding and Solving the Hadamard Population Conjecture
We describe our process for finding and solving the Hadamard Population conjecture. This conjecture is for all v, for all w, fht(v) dot-product fht(w) = n * population(v intersect w), where v and w are binary vectors and n is the length of all vectors. This is a submission to the #SoME2 co
From playlist Summer of Math Exposition 2 videos
C Programming: Quantum Computing
Learn a bit about one of the next waves in computer science: quantum computing. What kinds of problems can it solve more efficiently? We'll discuss some of the basic quantum operations and write a simulator in C.
From playlist C Programming
Today, we take a look at how we can represent complex numbers in matrix form.
From playlist Complex Analysis
Wolfram Physics Project: Exploring Quantum Computing Tuesday, May 18, 2021
This is a Wolfram Physics Project working session exploring quantum computing in the Wolfram Model. Begins at 6:50 Originally livestreamed at: https://twitch.tv/stephen_wolfram Stay up-to-date on this project by visiting our website: http://wolfr.am/physics Check out the announcemen
From playlist Wolfram Physics Project Livestream Archive
14C Matrices with Complex Number Elements
Matrix arithmetic with complex number elements.
From playlist Linear Algebra