Unsolved problems in mathematics | Matrix theory | Conjectures

Crouzeix's conjecture

Crouzeix's conjecture is an unsolved (as of 2018) problem in matrix analysis. It was proposed by Michel Crouzeix in 2004, and it refines Crouzeix's theorem, which states: where the set is the field of values of a n×n (i.e. square) complex matrix and is a complex function, that is analytic in the interior of and continuous up to the boundary of . The constant is independent of the matrix dimension, thus transferable to infinite-dimensional settings. The not yet proved conjecture states that the constant is sharpable to : Michel Crouzeix and Cesar Palencia proved in 2017 that the result holds for , improving the original constant of . Slightly reformulated, the conjecture can be stated as follows: For all square complex matrices and all complex polynomials : holds, where the norm on the left-hand side is the spectral operator 2-norm. While the general case is unknown, it is known that the conjecture holds for tridiagonal 3×3 matrices with elliptic field of values centered at an eigenvalue and for general n×n matrices that are nearly Jordan blocks. Furthermore, Anne Greenbaum and Michael L. Overton provided numerical support for Crouzeix's conjecture. (Wikipedia).

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What is the Riemann Hypothesis?

This video provides a basic introduction to the Riemann Hypothesis based on the the superb book 'Prime Obsession' by John Derbyshire. Along the way I look at convergent and divergent series, Euler's famous solution to the Basel problem, and the Riemann-Zeta function. Analytic continuation

From playlist Mathematics

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Stefan Sauter: A Family of Crouzeix-Raviart Non-Conforming Finite ...

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From playlist HIM Lectures: Trimester Program "Multiscale Problems"

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A (compelling?) reason for the Riemann Hypothesis to be true #SOME2

A visual walkthrough of the Riemann Zeta function and a claim of a good reason for the truth of the Riemann Hypothesis. This is not a formal proof but I believe the line of argument could lead to a formal proof.

From playlist Summer of Math Exposition 2 videos

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Proof that the Sequence {1/n} is a Cauchy Sequence

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Sequence {1/n} is a Cauchy Sequence

From playlist Cauchy Sequences

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C35 The Cauchy Euler Equation

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From playlist Differential Equations

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Real numbers and Cauchy sequences of rationals(I) | Real numbers and limits Math Foundations 111

We introduce the idea of a `Cauchy sequence of rational numbers'. The notion is in fact logically problematic. It involves epsilons and N's, much as does the notion of a limit, and suffers from similiar issues: how to guarantee that we can find an infinite number of N's for an infinite num

From playlist Math Foundations

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From playlist Complex Analysis

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From playlist Bernoulli Differential Equations

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Cauchy-Riemann Equations: Proving a Function is Nowhere Differentiable 1

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Using the Cauchy-Riemann Equations to prove that the function f(z) = conjugate(z) is nowhere differentiable. This is a straightforward application of the C.R. equations.

From playlist Complex Analysis

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C43 Example problem solving a Cauchy Euler equation

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From playlist Differential Equations

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Recent developments in non-commutative Iwasawa theory I - David Burns

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From playlist Mathematics

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Giles Gardam: Kaplansky's conjectures

Talk by Giles Gardam in the Global Noncommutative Geometry Seminar (Americas) https://globalncgseminar.org/talks/3580/ on September 17, 2021.

From playlist Global Noncommutative Geometry Seminar (Americas)

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Giles Gardam - Kaplansky's conjectures

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From playlist Talks of Mathematics Münster's reseachers

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Gonçalo Tabuada - 1/3 Noncommutative Counterparts of Celebrated Conjectures

Some celebrated conjectures of Beilinson, Grothendieck, Kimura, Tate, Voevodsky, Weil, and others, play a key central role in algebraic geometry. Notwithstanding the effort of several generations of mathematicians, the proof of (the majority of) these conjectures remains illusive. The aim

From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Explicit formulae for Gross-Stark units and Hilbert’s 12th problem by Mahesh Kakde

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From playlist Perfectoid Spaces 2019

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Explicit formulae for Stark Units and Hilbert's 12th problem - Samit Dasgupta

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From playlist Mathematics

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Gonçalo Tabuada - 3/3 Noncommutative Counterparts of Celebrated Conjectures

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From playlist Summer School 2020: Motivic, Equivariant and Non-commutative Homotopy Theory

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Lillian Ratliff - Learning via Conjectural Variations - IPAM at UCLA

Recorded 15 February 2022. Lillian Ratliff of the University of Washington presents "Learning via Conjectural Variations" at IPAM's Mathematics of Collective Intelligence Workshop. Learn more online at: http://www.ipam.ucla.edu/programs/workshops/mathematics-of-intelligences/?tab=schedule

From playlist Workshop: Mathematics of Collective Intelligence - Feb. 15 - 19, 2022.

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Teach Astronomy - Testing a Hypothesis

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From playlist 01. Fundamentals of Science and Astronomy

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Iwasawa theory of the fine Selmer groups of Galois representations by Sujatha Ramdorai

PERFECTOID SPACES ORGANIZERS: Debargha Banerjee, Denis Benois, Chitrabhanu Chaudhuri, and Narasimha Kumar Cheraku DATE & TIME: 09 September 2019 to 20 September 2019 VENUE: Madhava Lecture Hall, ICTS, Bangalore Scientific committee: Jacques Tilouine (University of Paris, France) Eknath

From playlist Perfectoid Spaces 2019

Related pages

Square matrix | Matrix analysis