Exploring the implications of the uncertainty relationships in quantum mechanics
Frontiers in Physics, 2022 Heisenberg guessed, after he established the matrix quantum mechanics, that the non-commutativity of the matrices of position and momentum implied that the position and momentum of a particle could not be precisely simultaneously determined.
Huai-Yu Wang
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The role of integer matrices in multidimensional multirate systems [PDF]
, 1993 The basic building blocks in a multidimensional (MD) multirate system are the decimation matrix M and the expansion matrix L. For the D-dimensional case these are D×D nonsingular integer matrices.
Chen, Tsuhan, Vaidyanathan, P. P.
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The Analytic Hierarchy Process, Max Algebra and Multi-objective Optimisation [PDF]
, 2012 The Analytic Hierarchy Process (AHP) is widely used for decision making involving multiple criteria. Elsner and van den Driessche introduced a max-algebraic approach to the single criterion AHP.
Baccelli +29 more
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Spectrum and commutativity preserving mappings on triangular matrices
Linear Algebra and Its Applications, 2002 T. Petek
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Boundary control for the processes, described by hyperbolic systems
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013 The boundary control problem for the system of hyperbolic equations with the mixed derivative is considered.The control is provided by the displacement (in the conditions of the first boundary-value problem).The coefficient matrices of different ...
Aleksandr Anatol'evich Andreev +2 more
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B\"acklund Transformation for the BC-Type Toda Lattice [PDF]
, 2007 We study an integrable case of n-particle Toda lattice: open chain with boundary terms containing 4 parameters. For this model we construct a B\"acklund transformation and prove its basic properties: canonicity, commutativity and spectrality.
Kuznetsov, Vadim, Sklyanin, Evgeny
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Sets of Semi-Commutative Matrices [PDF]
Proceedings of the Edinburgh Mathematical Society, 1933 In a paper entitled “Sets of anticommuting matrices” Eddington proved that if El, E2, …., Eqform a set of q four-rowed square matrices satisfying the relations,,where E is the unit matrix, then the maximum value of q is five. Later Newman showed that this result is a particular case of the general theorem that ifE1, E2, …., Eqform a set of q t-rowed ...
openaire +2 more sources
Representation of doubly infinite matrices as non-commutative Laurent series
Special Matrices, 2017 We present a new way to deal with doubly infinite lower Hessenberg matrices based on the representation of the matrices as the sum of their diagonal submatrices.
Arenas-Herrera María Ivonne +1 more
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Metrics on unitary matrices and their application to quantifying the degree of non-commutativity between unitary matrices [PDF]
Quantum information & computation, 2010 By studying the minimum resources required to perform a unitary transformation, families of metrics and pseudo-metrics on unitary matrices that are closely related to a recently reported quantum speed limit by the author are found.
H. Chau
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Integrability in three dimensions: Algebraic Bethe ansatz for anyonic models
Nuclear Physics B, 2015 We extend basic properties of two dimensional integrable models within the Algebraic Bethe Ansatz approach to 2+1 dimensions and formulate the sufficient conditions for the commutativity of transfer matrices of different spectral parameters, in analogy ...
Sh. Khachatryan +3 more
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