An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices

Autor: Hutchinson George

Publikováno v: Special Matrices, Vol 9, Iss 1, Pp 83-102 (2021)

A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.

Externí odkaz: https://doaj.org/article/e017fa3f8f3c403d8cdb939d7a8fd906

Unification of the Nature’s Complexities via a Matrix Permanent—Critical Phenomena, Fractals, Quantum Computing, ♯P-Complexity

Autor: Vitaly Kocharovsky, Vladimir Kocharovsky, Sergey Tarasov

Publikováno v: Entropy, Vol 22, Iss 3, p 322 (2020)

We reveal the analytic relations between a matrix permanent and major nature’s complexities manifested in critical phenomena, fractal structures and chaos, quantum information processes in many-body physics, number-theoretic complexity in mathemati

Externí odkaz: https://doaj.org/article/c2c8d27b9c664b6d80f71cf6620bb669

An elementary proof of Chollet’s permanent conjecture for 4 × 4 real matrices

Autor: George Hutchinson

Publikováno v: Special Matrices, Vol 9, Iss 1, Pp 83-102 (2021)

A proof of the statement per(A ∘ B) ≤ per(A)per(B) is given for 4 × 4 positive semidefinite real matrices. The proof uses only elementary linear algebra and a rather lengthy series of simple inequalities.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97fff79eeee685f988498fc85548a796
https://doaj.org/article/e017fa3f8f3c403d8cdb939d7a8fd906

The m-Bézout Bound and Distance Geometry

Autor: Ioannis Z. Emiris, Evangelos Bartzos, Charalambos Tzamos

Publikováno v: CASC 2021-23rd International Workshop Computer Algebra in Scientific Computing
CASC 2021-23rd International Workshop Computer Algebra in Scientific Computing, Sep 2021, Sochi, Russia. ⟨10.1007/978-3-030-85165-1_2⟩
Computer Algebra in Scientific Computing ISBN: 9783030851644
CASC

International audience; We offer a closed form bound on the m-Bézout bound for multi-homogeneous systems whose equations include two variable subsets of the same degree. Our bound is expectedly not tight, since computation of the m-Bézout number is

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0bc038729e88a760b6d40fb82ca6e69c
https://hal.science/hal-03523833

Complex Matrix Scalings, Extremal Permanents, and the Geometric Measure of Entanglement

Autor: Hutchinson, George

An n x n matrix with complex entries is said to be doubly quasi-stochastic (DQS) if all row and column sums are equal to one. Given a positive definite matrix A and a diagonal matrix D, we say that D*AD is a (complex matrix) scaling of A if D*AD is d

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=od_______453::2e04d5416781b92f9c93e9e229c169ba
https://hdl.handle.net/10214/12988