Matrices

Complex Hadamard matrix

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).

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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

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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

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Complex Numbers as Matrices

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From playlist Complex Numbers

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From playlist Linear Algebra for Computer Scientists

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From playlist MIT 6.451 Principles of Digital Communication II

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Christian Bär: Local index theory for Lorentzian manifolds

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From playlist Mathematical Physics

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

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From playlist Virtual Conference

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Quantum computation (Lecture 02) by Peter Young

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

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From playlist Daily Study Group: Quantum Computation Framework

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

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From playlist Summer of Math Exposition 2 videos

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From playlist C Programming

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From playlist Complex Analysis

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From playlist Wolfram Physics Project Livestream Archive

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From playlist Linear Algebra

Related pages

Orthogonal matrix | DFT matrix | Complex number | Conjugate transpose | Butson-type Hadamard matrix | Matrix (mathematics) | Hadamard matrix | Permutation matrix | Unitary matrix | Operator algebra