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Relevant bibliographies by topics / Unipotent Matrix

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Academic literature on the topic 'Unipotent Matrix'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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Journal articles on the topic "Unipotent Matrix"

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Călugăreanu, Grigore. "Unipotent similarity for matrices over commutative domains." Acta Universitatis Sapientiae, Mathematica 16, no. 1 (2025): 86–92. https://doi.org/10.47745/ausm-2024-0006.

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A unit u of a ring is called unipotent if u − 1 is nilpotent. We characterize the similarity of 2×2 matrices over commutative domains, realized by unipotent matrices, i.e., B = U−1AU with unipotent matrix U.

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Wehrfritz, B. A. F. "Unipotent normal subgroups of skew linear groups." Mathematical Proceedings of the Cambridge Philosophical Society 105, no. 1 (1989): 37–51. http://dx.doi.org/10.1017/s0305004100001341.

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A recurrent problem over many years in the study of linear groups has been the determination of the central height of a unipotent normal subgroup of some matrix group of specified type. In the theory of matrix groups over division rings, unipotent elements frequently present special difficulties and these have usually been by-passed by the addition of some suitable hypothesis. In this paper we make a start on the removal of these extraneous hypotheses. Our motivation for doing this now conies from [9], where by 3·7 of that paper the additional assumptions have finally reduced us to degree one,

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3

DIACONIS, Persi, and Robert HOUGH. "Random walk on unipotent matrix groups." Annales scientifiques de l'École Normale Supérieure 54, no. 3 (2021): 587–625. http://dx.doi.org/10.24033/asens.2466.

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Duan, Xiaomin, Huafei Sun, and Linyu Peng. "Riemannian Means on Special Euclidean Group and Unipotent Matrices Group." Scientific World Journal 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/292787.

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Among the noncompact matrix Lie groups, the special Euclidean group and the unipotent matrix group play important roles in both theoretic and applied studies. The Riemannian means of a finite set of the given points on the two matrix groups are investigated, respectively. Based on the left invariant metric on the matrix Lie groups, the geodesic between any two points is gotten. And the sum of the geodesic distances is taken as the cost function, whose minimizer is the Riemannian mean. Moreover, a Riemannian gradient algorithm for computing the Riemannian mean on the special Euclidean group and

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PIKUŁA, RAFAŁ. "Enveloping semigroups of unipotent affine transformations of the torus." Ergodic Theory and Dynamical Systems 30, no. 5 (2010): 1543–59. http://dx.doi.org/10.1017/s0143385709000261.

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AbstractWe provide a description of the enveloping semigroup of the affine unipotent transformation T:X→X of the form T(x)=Ax+α, where A is a lower triangular unipotent matrix, α is a constant vector, and X is a finite-dimensional torus. In particular, we show that in this case the enveloping semigroup is a nilpotent group whose nilpotency class is at most the dimension of the underlying torus.

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Hou, Xin, Zhengyi Xiao, Yajing Hao, and Qi Yuan. "Decomposition of symplectic matrices into products of symplectic unipotent matrices of index 2." Electronic Journal of Linear Algebra 35 (November 14, 2019): 497–502. http://dx.doi.org/10.13001/1081-3810.4063.

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In this article, it is proved that every symplectic matrix can be decomposed into a product of three symplectic unipotent matrices of index 2, i.e., every complex matrix A satisfying ATJA = J with J = [0 -

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Testerman, Donna M., and Alexandre E. Zalesski. "Irreducible representations of simple algebraic groups in which a unipotent element is represented by a matrix with a single non-trivial Jordan block." Journal of Group Theory 21, no. 1 (2018): 1–20. http://dx.doi.org/10.1515/jgth-2017-0019.

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AbstractLetGbe a simply connected simple linear algebraic group of exceptional Lie type over an algebraically closed fieldFof characteristic{p\geq 0}, and let{u\in G}be a nonidentity unipotent element. Let ϕ be a non-trivial irreducible representation ofG. Then the Jordan normal form of{\phi(u)}contains at most one non-trivial block if and only ifGis of type{G_{2}},uis a regular unipotent element and{\dim\phi\leq 7}. Note that the irreducible representations of the simple classical algebraic groups in which a non-trivial unipotent element is represented by a matrix whose Jordan form has a sing

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Feng, Zhicheng, and Britta Späth. "Unitriangular basic sets, Brauer characters and coprime actions." Representation Theory of the American Mathematical Society 27, no. 6 (2023): 115–48. http://dx.doi.org/10.1090/ert/635.

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We show that the decomposition matrix of a given group G G is unitriangular, whenever G G has a normal subgroup N N such that the decomposition matrix of N N is unitriangular, G / N G/N is abelian and certain characters of N N extend to their stabilizer in G G . Using the recent result by Brunat–Dudas–Taylor establishing that unipotent blocks have a unitriangular decomposition matrix, this allows us to prove that blocks of groups of quasi-simple groups of Lie type have a unitriangular decomposition matrix whenever they are related via Bonnafé–Dat–Rouquier’s equivalence to a unipotent block. Th

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Mennicke, Jens. "A Remark on the Congruence Subgroup Problem." MATHEMATICA SCANDINAVICA 86, no. 2 (2000): 206. http://dx.doi.org/10.7146/math.scand.a-14289.

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In the theory of congruence subgroups, one usually shows that, under suitable assumptions, the normal closure of the mth power of an elementary unipotent matrix coincides with the full con- gruence subgroup mod m. For applications, it is sometimes useful to study the subgroup generated by the mth powers of the elementary unipotent elements. We give an elementary proof for the fact that in $SL_n(Z)$ for $n > 3$, this subgroup is normal in a suitably defined congruence subgroup of $SL_n(Z)$ .

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10

Thompson, J. G. "Unipotent Elements, Standard Involutions, and the Divisor Matrix." Communications in Algebra 36, no. 9 (2008): 3363–71. http://dx.doi.org/10.1080/00927870802107546.

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Dissertations / Theses on the topic "Unipotent Matrix"

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Buenger, Carl D. Buenger. "Quantitative Non-Divergence, Effective Mixing, and Random Walks on Homogeneous Spaces." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1462800914.

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Gaoseb, Frans Otto. "Spectral factorization of matrices." Diss., 2020. http://hdl.handle.net/10500/26844.

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Abstract in English<br>The research will analyze and compare the current research on the spectral factorization of non-singular and singular matrices. We show that a nonsingular non-scalar matrix A can be written as a product A = BC where the eigenvalues of B and C are arbitrarily prescribed subject to the condition that the product of the eigenvalues of B and C must be equal to the determinant of A. Further, B and C can be simultaneously triangularised as a lower and upper triangular matrix respectively. Singular matrices will be factorized in terms of nilpotent matrices and otherwise over

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Book chapters on the topic "Unipotent Matrix"

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Garima, Asmita Deka Dey, and Arun Kumar. "Introduction." In Carrier-mediated Gene and Drug Delivery for Dermal Wound Healing. Royal Society of Chemistry, 2023. http://dx.doi.org/10.1039/9781837671540-00001.

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One of the most intricate bodily processes is the healing of dermal wounds. Multiple cell types with different roles during the phases of hemostasis, inflammation, growth, re-epithelialization and remodelling must be coordinated in both space and time. Phenotypic and functional variability within a few of these cell types have been discovered as a result of the development of single-cell technologies. Rare stem cell subgroups that are unipotent in the undamaged state but become multipotent after skin injury have also been found to exist within the skin. Dermal wound healing is adversely affect

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