The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Zur Izhakian - One of the best experts on this subject based on the ideXlab platform.
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supertropical Matrix Algebra ii solving tropical equations
Israel Journal of Mathematics, 2011Co-Authors: Zur Izhakian, Louis RowenAbstract:We continue the study of matrices over a supertropical Algebra, proving the existence of a tangible adjoint of A, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity Matrix corresponding to A; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer’s rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an n × n Matrix has n distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.
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supertropical Matrix Algebra iii powers of matrices and generalized eigenspaces
arXiv: Commutative Algebra, 2010Co-Authors: Zur Izhakian, Louis RowenAbstract:We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power of a Matrix. This leads to a Jordan-type decomposition of supertropical matrices, together with a generalized eigenspace decomposition of a power of an arbitrary supertropical Matrix.
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tropical arithmetic and Matrix Algebra
Communications in Algebra, 2009Co-Authors: Zur IzhakianAbstract:This article introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e., summation and maximum. Although our framework is combinatorial, notions of regularity and invertibility arise naturally for matrices over this semiring; we show that a tropical Matrix is invertible if and only if it is regular.
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supertropical Matrix Algebra ii solving tropical equations
arXiv: Commutative Algebra, 2009Co-Authors: Zur Izhakian, Louis RowenAbstract:We continue the study of matrices over a supertropical Algebra, proving the existence of a tangible adjoint of $A$, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity Matrix corresponding to $A$; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer's rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an $n\times n$ Matrix has $n$ distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.
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supertropical Matrix Algebra
arXiv: Commutative Algebra, 2008Co-Authors: Zur Izhakian, Louis RowenAbstract:The objective of this paper is to develop a general Algebraic theory of supertropical Matrix Algebra, extending [11]. Our main results are as follows: * The tropical determinant (i.e., permanent) is multiplicative when all the determinants involved are tangible. * There exists an adjoint Matrix $\adj{A}$ such that the Matrix $A \adj{A}$ behaves much like the identity Matrix (times $|A|$). * Every Matrix $A$ is a supertropical root of its Hamilton-Cayley polynomial $f_A$. If these roots are distinct, then $A$ is conjugate (in a certain supertropical sense) to a diagonal Matrix. * The tropical determinant of a Matrix $A$ is a ghost iff the rows of $A$ are tropically dependent, iff the columns of $A$ are tropically dependent. * Every root of $f_A$ is a "supertropical" eigenvalue of $A$ (appropriately defined), and has a tangible supertropical eigenvector.
Louis Rowen - One of the best experts on this subject based on the ideXlab platform.
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supertropical Matrix Algebra ii solving tropical equations
Israel Journal of Mathematics, 2011Co-Authors: Zur Izhakian, Louis RowenAbstract:We continue the study of matrices over a supertropical Algebra, proving the existence of a tangible adjoint of A, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity Matrix corresponding to A; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer’s rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an n × n Matrix has n distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.
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supertropical Matrix Algebra iii powers of matrices and generalized eigenspaces
arXiv: Commutative Algebra, 2010Co-Authors: Zur Izhakian, Louis RowenAbstract:We investigate powers of supertropical matrices, with special attention to the role of the coefficients of the supertropical characteristic polynomial (especially the supertropical trace) in controlling the rank of a power of a Matrix. This leads to a Jordan-type decomposition of supertropical matrices, together with a generalized eigenspace decomposition of a power of an arbitrary supertropical Matrix.
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supertropical Matrix Algebra ii solving tropical equations
arXiv: Commutative Algebra, 2009Co-Authors: Zur Izhakian, Louis RowenAbstract:We continue the study of matrices over a supertropical Algebra, proving the existence of a tangible adjoint of $A$, which provides the unique right (resp. left) quasi-inverse maximal with respect to the right (resp. left) quasi-identity Matrix corresponding to $A$; this provides a unique maximal (tangible) solution to supertropical vector equations, via a version of Cramer's rule. We also describe various properties of this tangible adjoint, and use it to compute supertropical eigenvectors, thereby producing an example in which an $n\times n$ Matrix has $n$ distinct supertropical eigenvalues but their supertropical eigenvectors are tropically dependent.
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supertropical Matrix Algebra
arXiv: Commutative Algebra, 2008Co-Authors: Zur Izhakian, Louis RowenAbstract:The objective of this paper is to develop a general Algebraic theory of supertropical Matrix Algebra, extending [11]. Our main results are as follows: * The tropical determinant (i.e., permanent) is multiplicative when all the determinants involved are tangible. * There exists an adjoint Matrix $\adj{A}$ such that the Matrix $A \adj{A}$ behaves much like the identity Matrix (times $|A|$). * Every Matrix $A$ is a supertropical root of its Hamilton-Cayley polynomial $f_A$. If these roots are distinct, then $A$ is conjugate (in a certain supertropical sense) to a diagonal Matrix. * The tropical determinant of a Matrix $A$ is a ghost iff the rows of $A$ are tropically dependent, iff the columns of $A$ are tropically dependent. * Every root of $f_A$ is a "supertropical" eigenvalue of $A$ (appropriately defined), and has a tangible supertropical eigenvector.
A Georgakilas - One of the best experts on this subject based on the ideXlab platform.
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optical characterization of free electron concentration in heteroepitaxial inn layers using fourier transform infrared spectroscopy and a 2 2 transfer Matrix Algebra
Journal of Applied Physics, 2013Co-Authors: C C Katsidis, A O Ajagunna, A GeorgakilasAbstract:Fourier Transform Infrared (FTIR) reflectance spectroscopy has been implemented as a non-destructive, non-invasive, tool for the optical characterization of a set of c-plane InN single heteroepitaxial layers spanning a wide range of thicknesses (30–2000 nm). The c-plane (0001) InN epilayers were grown by plasma-assisted molecular beam epitaxy (PAMBE) on GaN(0001) buffer layers which had been grown on Al2O3(0001) substrates. It is shown that for arbitrary multilayers with homogeneous anisotropic layers having their principal axes coincident with the laboratory coordinates, a 2 × 2 Matrix Algebra based on a general transfer-Matrix method (GTMM) is adequate to interpret their optical response. Analysis of optical reflectance in the far and mid infrared spectral range has been found capable to discriminate between the bulk, the surface and interface contributions of free carriers in the InN epilayers revealing the existence of electron accumulation layers with carrier concentrations in mid 1019 cm−3 at both t...
Harald E Moller - One of the best experts on this subject based on the ideXlab platform.
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Matrix Algebra based calculations of the time evolution of the binary spin bath model for magnetization transfer
Journal of Magnetic Resonance, 2013Co-Authors: D Muller, Andre Pampel, Harald E MollerAbstract:Abstract Quantification of magnetization-transfer (MT) experiments are typically based on the assumption of the binary spin-bath model. This model allows for the extraction of up to six parameters (relative pool sizes, relaxation times, and exchange rate constants) for the characterization of macromolecules, which are coupled via exchange processes to the water in tissues. Here, an approach is presented for estimating MT parameters acquired with arbitrary saturation schemes and imaging pulse sequences. It uses Matrix Algebra to solve the Bloch–McConnell equations without unwarranted simplifications, such as assuming steady-state conditions for pulsed saturation schemes or neglecting imaging pulses. The algorithm achieves sufficient efficiency for voxel-by-voxel MT parameter estimations by using a polynomial interpolation technique. Simulations, as well as experiments in agar gels with continuous-wave and pulsed MT preparation, were performed for validation and for assessing approximations in previous modeling approaches. In vivo experiments in the normal human brain yielded results that were consistent with published data.
Vsevolod Gubarev - One of the best experts on this subject based on the ideXlab platform.
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rota baxter operators of nonzero weight on the Matrix Algebra of order three
Linear & Multilinear Algebra, 2020Co-Authors: Maxim Goncharov, Vsevolod GubarevAbstract:We classify all Rota–Baxter operators of nonzero weight on the Matrix Algebra of order three over an Algebraically closed field of characteristic zero which do not arise from the decompositions of ...