Matrix semigroups with constant spectral radius
Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized by means of irreducible ones. Each irreducible c.s.r. semigro...
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| Published in: | Linear algebra and its applications Vol. 513; pp. 376 - 408 |
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| Language: | English |
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15.01.2017
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| ISSN: | 0024-3795, 1873-1856 |
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| Abstract | Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized by means of irreducible ones. Each irreducible c.s.r. semigroup defines walks on Euclidean sphere, all its nonsingular elements are similar (in the same basis) to orthogonal. We classify all nonnegative c.s.r. semigroups and arbitrary low-dimensional semigroups. For higher dimensions, we describe five classes and leave an open problem on completeness of that list. The problem of algorithmic recognition of c.s.r. property is proved to be polynomially solvable for irreducible semigroups and undecidable for reducible ones. |
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| AbstractList | Multiplicative matrix semigroups with constant spectral radius (c.s.r.) are studied and applied to several problems of algebra, combinatorics, functional equations, and dynamical systems. We show that all such semigroups are characterized by means of irreducible ones. Each irreducible c.s.r. semigroup defines walks on Euclidean sphere, all its nonsingular elements are similar (in the same basis) to orthogonal. We classify all nonnegative c.s.r. semigroups and arbitrary low-dimensional semigroups. For higher dimensions, we describe five classes and leave an open problem on completeness of that list. The problem of algorithmic recognition of c.s.r. property is proved to be polynomially solvable for irreducible semigroups and undecidable for reducible ones. |
| Author | Voynov, A.S. Protasov, V.Yu |
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| Cites_doi | 10.4064/aa-88-4-371-396 10.1016/j.laa.2013.01.034 10.1070/IM2004v068n03ABEH000489 10.1137/0523059 10.1145/1362542.1362547 10.1016/0024-3795(89)90495-3 10.1016/0024-3795(95)00544-7 10.1007/BF00969859 10.1090/mcom/3128 10.1007/BF01240749 10.1109/TAC.2008.2012009 10.1016/0304-3975(77)90001-9 10.1016/j.laa.2010.04.006 10.1007/BF01219774 10.1070/SM2013v204n08ABEH004332 10.1016/j.laa.2007.08.001 10.1070/SM2011v202n10ABEH004193 10.1070/SM2000v191n03ABEH000464 10.1137/11083808X 10.1137/S0036141092228179 10.4153/CJM-1995-053-x 10.1070/IM2006v070n05ABEH002335 10.1016/0024-3795(92)90267-E 10.1016/S0167-6911(00)00049-9 10.1016/0304-3975(77)90006-8 10.1134/S0037446612010053 10.1007/s10208-012-9121-0 10.1090/S1061-0022-07-00963-6 10.1070/IM1997v061n05ABEH000161 |
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| Keywords | Fractal curves Spectral radius 15B36 Convex body Finite matrix group Polynomial algorithm Linear switching systems 15A30 47D03 Multiplicative semigroup 15A60 Ellipsoid Joint spectral characteristics |
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| References | Villemoes (br0370) 1994; 25 Gaganov, Sheipak (br0100) 2012; 53 Longstaff, Radjavi (br0170) 1995; 47 Popov (br0260) 2013; 438 Liberzon (br0180) 2003 Protasov (br0290) 2006; 70 Micchelli, Prautzsch (br0210) 1989; 114–115 Zaguskin (br0400) 1958; 13 Molchanov, Pyatnitskii, Molchanov, Pyatnitskii, Molchanov, Pyatnitskii (br0220) 1986; 47 Barabanov (br0010) 1988; 49 Hartfiel (br0120) 2002 Protasov (br0410) 2004; 68 Lin, Antsaklis (br0190) 2009; 54 Protasov (br0320) 2016 Berger, Wang (br0040) 1992; 166 Protasov (br0300) 2007; 18 Radjavi, Rosenthal (br0330) 2000 Blondel, Tsitsiklis (br0050) 2000; 41 Barabanov (br0020) 1988; 29 Jungers, Protasov, Blondel (br0150) 2008; 428 Protasov (br0310) 2010; 433 Guglielmi, Protasov (br0110) 2013; 13 Omladič, Radjavi (br0250) 1997; 251 Crespi, Cybenko, Jiang (br0060) 2008; 4 Tsitsiklis, Blondel (br0360) 1997; 10 Daubechies, Lagarias (br0070) 1992; 23 Dumont, Sidorov, Thomas (br0080) 1999; 88 Jacob (br0140) 1977; 5 Protasov (br0280) 2000; 191 Fainshil, Margaliot (br0090) 2012; 50 Voynov (br0390) 2013; 204 Krein, Rutman (br0160) 1950 Voynov (br0380) 2010; 202 Mott, Schneider (br0230) 1959; 10 Reznick (br0340) 1990 Protasov (br0270) 1997; 61 Barnsley (br0030) 1988 Mc Naughton, Zalcstein (br0240) 1975; 34 Mandel, Simon (br0200) 1977; 5 Reznick (10.1016/j.laa.2016.10.013_br0340) 1990 Lin (10.1016/j.laa.2016.10.013_br0190) 2009; 54 Daubechies (10.1016/j.laa.2016.10.013_br0070) 1992; 23 Voynov (10.1016/j.laa.2016.10.013_br0380) 2010; 202 Voynov (10.1016/j.laa.2016.10.013_br0390) 2013; 204 Mott (10.1016/j.laa.2016.10.013_br0230) 1959; 10 Protasov (10.1016/j.laa.2016.10.013_br0280) 2000; 191 Barabanov (10.1016/j.laa.2016.10.013_br0020) 1988; 29 Protasov (10.1016/j.laa.2016.10.013_br0290) 2006; 70 Protasov (10.1016/j.laa.2016.10.013_br0270) 1997; 61 Gaganov (10.1016/j.laa.2016.10.013_br0100) 2012; 53 Popov (10.1016/j.laa.2016.10.013_br0260) 2013; 438 Blondel (10.1016/j.laa.2016.10.013_br0050) 2000; 41 Protasov (10.1016/j.laa.2016.10.013_br0320) 2016 Villemoes (10.1016/j.laa.2016.10.013_br0370) 1994; 25 Molchanov (10.1016/j.laa.2016.10.013_bib4D50s3) 1986; 47 Molchanov (10.1016/j.laa.2016.10.013_bib4D50s1) 1986; 47 Fainshil (10.1016/j.laa.2016.10.013_br0090) 2012; 50 Liberzon (10.1016/j.laa.2016.10.013_br0180) 2003 Protasov (10.1016/j.laa.2016.10.013_br0310) 2010; 433 Krein (10.1016/j.laa.2016.10.013_br0160) 1950 Crespi (10.1016/j.laa.2016.10.013_br0060) 2008; 4 Hartfiel (10.1016/j.laa.2016.10.013_br0120) 2002 Micchelli (10.1016/j.laa.2016.10.013_br0210) 1989; 114–115 Barabanov (10.1016/j.laa.2016.10.013_br0010) 1988; 49 Radjavi (10.1016/j.laa.2016.10.013_br0330) 2000 Protasov (10.1016/j.laa.2016.10.013_br0410) 2004; 68 Jungers (10.1016/j.laa.2016.10.013_br0150) 2008; 428 Jacob (10.1016/j.laa.2016.10.013_br0140) 1977; 5 Mandel (10.1016/j.laa.2016.10.013_br0200) 1977; 5 Zaguskin (10.1016/j.laa.2016.10.013_br0400) 1958; 13 Longstaff (10.1016/j.laa.2016.10.013_br0170) 1995; 47 Mc Naughton (10.1016/j.laa.2016.10.013_br0240) 1975; 34 Protasov (10.1016/j.laa.2016.10.013_br0300) 2007; 18 Tsitsiklis (10.1016/j.laa.2016.10.013_br0360) 1997; 10 Omladič (10.1016/j.laa.2016.10.013_br0250) 1997; 251 Barnsley (10.1016/j.laa.2016.10.013_br0030) 1988 Guglielmi (10.1016/j.laa.2016.10.013_br0110) 2013; 13 Berger (10.1016/j.laa.2016.10.013_br0040) 1992; 166 Dumont (10.1016/j.laa.2016.10.013_br0080) 1999; 88 Molchanov (10.1016/j.laa.2016.10.013_bib4D50s2) 1986; 47 |
| References_xml | – volume: 29 start-page: 521 year: 1988 end-page: 530 ident: br0020 article-title: Absolute characteristic exponent of a class of linear nonstationary systems of differential equations publication-title: Sib. Math. J. – volume: 34 start-page: 202 year: 1975 end-page: 299 ident: br0240 article-title: The Burnside problem for semigroups publication-title: J. Algebra – volume: 204 start-page: 1122 year: 2013 end-page: 1130 ident: br0390 article-title: On the structure of self-affine convex bodies publication-title: Sb. Math. – year: 1988 ident: br0030 article-title: Fractals Everywhere – year: 2016 ident: br0320 article-title: The Euler binary partition function and subdivision schemes publication-title: Math. Comp. – volume: 4 start-page: 1 year: 2008 end-page: 42 ident: br0060 article-title: The theory of trackability with applications to sensor networks publication-title: ACM Trans. Sensor Networks – volume: 68 start-page: 139 year: 2004 end-page: 180 ident: br0410 article-title: On the regularity of de Rham curves publication-title: Izv. Math. – year: 2003 ident: br0180 article-title: Switching in Systems and Control – volume: 10 start-page: 31 year: 1997 end-page: 40 ident: br0360 article-title: The Lyapunov exponent and joint spectral radius of pairs of matrices are hard – when not impossible – to compute and to approximate publication-title: Math. Control Signals Systems – volume: 202 start-page: 1413 year: 2010 end-page: 1439 ident: br0380 article-title: Self-affine polytopes. Applications to functional equations and matrix theory publication-title: Sb. Math. – volume: 53 start-page: 55 year: 2012 end-page: 71 ident: br0100 article-title: A boundedness criterion for the variations of self-similar functions publication-title: Sib. Math. J. – year: 1950 ident: br0160 article-title: Linear operators leaving invariant a cone in a Banach space publication-title: Amer. Math. Soc. Transl. – volume: 23 start-page: 1031 year: 1992 end-page: 1079 ident: br0070 article-title: Two-scale difference equations, II: local regularity, infinite products of matrices and fractals publication-title: SIAM J. Math. Anal. – volume: 70 start-page: 123 year: 2006 end-page: 162 ident: br0290 article-title: Fractal curves and wavelets publication-title: Izv. Math. – start-page: 451 year: 1990 end-page: 477 ident: br0340 article-title: Some binary partition functions publication-title: Analytic Number Theory: Proceedings of a Conference in Honor of Paul T. Bateman – volume: 47 start-page: 1007 year: 1995 end-page: 1022 ident: br0170 article-title: On permutability and submultiplicativity of spectral radius publication-title: Canad. J. Math. – volume: 47 start-page: 344 year: 1986 end-page: 354 ident: br0220 article-title: Lyapunov functions, defining necessary and sufficient conditions for the absolute stability of nonlinear nonstationary control systems, I publication-title: Autom. Remote Control – volume: 88 start-page: 371 year: 1999 end-page: 396 ident: br0080 article-title: Number of representations related to a linear recurrent basis publication-title: Acta Arith. – volume: 54 start-page: 308 year: 2009 end-page: 322 ident: br0190 article-title: Stability and stabilizability of switched linear systems: a survey of recent results publication-title: IEEE Trans. Automat. Control – volume: 10 start-page: 1 year: 1959 end-page: 6 ident: br0230 article-title: Matrix algebras and groups relatively bounded in norms publication-title: Arch. Math. (Basel) – volume: 428 start-page: 2296 year: 2008 end-page: 2312 ident: br0150 article-title: Efficient algorithms for deciding the type of growth of products of integer matrices publication-title: Linear Algebra Appl. – volume: 251 start-page: 59 year: 1997 end-page: 72 ident: br0250 article-title: Irreducible semigroups with multiplicative spectral radius publication-title: Linear Algebra Appl. – year: 2000 ident: br0330 article-title: Simultaneous Triangularization – volume: 13 start-page: 37 year: 2013 end-page: 97 ident: br0110 article-title: Exact computation of joint spectral characteristics of linear operators publication-title: Found. Comput. Math. – volume: 5 start-page: 183 year: 1977 end-page: 204 ident: br0140 article-title: Un algorithme calculant le cardinal, fini ou infini, des demi-groupes de matrices publication-title: Theoret. Comput. Sci. – volume: 114–115 start-page: 841 year: 1989 end-page: 870 ident: br0210 article-title: Uniform refinement of curves publication-title: Linear Algebra Appl. – volume: 49 start-page: 152 year: 1988 end-page: 157 ident: br0010 article-title: Lyapunov indicator for discrete inclusions, I–III publication-title: Autom. Remote Control – volume: 166 start-page: 21 year: 1992 end-page: 27 ident: br0040 article-title: Bounded semigroups of matrices publication-title: Linear Algebra Appl. – year: 2002 ident: br0120 article-title: Nonhomogeneous Matrix Products – volume: 438 start-page: 4439 year: 2013 end-page: 4447 ident: br0260 article-title: On matrix semigroups bounded above and below publication-title: Linear Algebra Appl. – volume: 50 start-page: 2193 year: 2012 end-page: 2215 ident: br0090 article-title: A maximum principle for the stability analysis of positive bilinear control systems with applications to positive linear switched systems publication-title: SIAM J. Control Optim. – volume: 433 start-page: 781 year: 2010 end-page: 789 ident: br0310 article-title: When do several linear operators share an invariant cone? publication-title: Linear Algebra Appl. – volume: 191 start-page: 381 year: 2000 end-page: 414 ident: br0280 article-title: Asymptotic behavior of the partition function publication-title: Sb. Math. – volume: 5 start-page: 101 year: 1977 end-page: 111 ident: br0200 article-title: On finite semigroups of matrices publication-title: Theoret. Comput. Sci. – volume: 13 start-page: 89 year: 1958 end-page: 93 ident: br0400 article-title: Circumscribed and inscribed ellipsoids of extremal volume publication-title: Uspekhi Mat. Nauk – volume: 41 start-page: 135 year: 2000 end-page: 140 ident: br0050 article-title: The boundedness of all products of a pair of matrices is undecidable publication-title: Systems Control Lett. – volume: 61 start-page: 995 year: 1997 end-page: 1030 ident: br0270 article-title: The generalized spectral radius. A geometric approach publication-title: Izv. Math. – volume: 18 start-page: 607 year: 2007 end-page: 646 ident: br0300 article-title: Spectral decomposition of 2-block Toeplitz matrices and refinement equations publication-title: St. Petersburg Math. J. – volume: 25 start-page: 1433 year: 1994 end-page: 1460 ident: br0370 article-title: Wavelet analysis of refinement equations publication-title: SIAM J. Math. Anal. – volume: 88 start-page: 371 year: 1999 ident: 10.1016/j.laa.2016.10.013_br0080 article-title: Number of representations related to a linear recurrent basis publication-title: Acta Arith. doi: 10.4064/aa-88-4-371-396 – volume: 49 start-page: 152 issue: 2 year: 1988 ident: 10.1016/j.laa.2016.10.013_br0010 article-title: Lyapunov indicator for discrete inclusions, I–III publication-title: Autom. Remote Control – issue: 26 year: 1950 ident: 10.1016/j.laa.2016.10.013_br0160 article-title: Linear operators leaving invariant a cone in a Banach space publication-title: Amer. Math. Soc. Transl. – volume: 438 start-page: 4439 issue: 11 year: 2013 ident: 10.1016/j.laa.2016.10.013_br0260 article-title: On matrix semigroups bounded above and below publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2013.01.034 – volume: 68 start-page: 139 issue: 3 year: 2004 ident: 10.1016/j.laa.2016.10.013_br0410 article-title: On the regularity of de Rham curves publication-title: Izv. Math. doi: 10.1070/IM2004v068n03ABEH000489 – volume: 23 start-page: 1031 issue: 4 year: 1992 ident: 10.1016/j.laa.2016.10.013_br0070 article-title: Two-scale difference equations, II: local regularity, infinite products of matrices and fractals publication-title: SIAM J. Math. Anal. doi: 10.1137/0523059 – volume: 13 start-page: 89 year: 1958 ident: 10.1016/j.laa.2016.10.013_br0400 article-title: Circumscribed and inscribed ellipsoids of extremal volume publication-title: Uspekhi Mat. Nauk – volume: 4 start-page: 1 issue: 3 year: 2008 ident: 10.1016/j.laa.2016.10.013_br0060 article-title: The theory of trackability with applications to sensor networks publication-title: ACM Trans. Sensor Networks doi: 10.1145/1362542.1362547 – volume: 114–115 start-page: 841 year: 1989 ident: 10.1016/j.laa.2016.10.013_br0210 article-title: Uniform refinement of curves publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(89)90495-3 – volume: 251 start-page: 59 year: 1997 ident: 10.1016/j.laa.2016.10.013_br0250 article-title: Irreducible semigroups with multiplicative spectral radius publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(95)00544-7 – volume: 29 start-page: 521 year: 1988 ident: 10.1016/j.laa.2016.10.013_br0020 article-title: Absolute characteristic exponent of a class of linear nonstationary systems of differential equations publication-title: Sib. Math. J. doi: 10.1007/BF00969859 – year: 2016 ident: 10.1016/j.laa.2016.10.013_br0320 article-title: The Euler binary partition function and subdivision schemes publication-title: Math. Comp. doi: 10.1090/mcom/3128 – volume: 10 start-page: 1 year: 1959 ident: 10.1016/j.laa.2016.10.013_br0230 article-title: Matrix algebras and groups relatively bounded in norms publication-title: Arch. Math. (Basel) doi: 10.1007/BF01240749 – volume: 54 start-page: 308 issue: 2 year: 2009 ident: 10.1016/j.laa.2016.10.013_br0190 article-title: Stability and stabilizability of switched linear systems: a survey of recent results publication-title: IEEE Trans. Automat. Control doi: 10.1109/TAC.2008.2012009 – volume: 5 start-page: 101 year: 1977 ident: 10.1016/j.laa.2016.10.013_br0200 article-title: On finite semigroups of matrices publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(77)90001-9 – volume: 433 start-page: 781 issue: 4 year: 2010 ident: 10.1016/j.laa.2016.10.013_br0310 article-title: When do several linear operators share an invariant cone? publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2010.04.006 – volume: 47 start-page: 443 issue: 4 year: 1986 ident: 10.1016/j.laa.2016.10.013_bib4D50s2 article-title: Lyapunov functions, defining necessary and sufficient conditions for the absolute stability of nonlinear nonstationary control systems, II publication-title: Autom. Remote Control – volume: 10 start-page: 31 year: 1997 ident: 10.1016/j.laa.2016.10.013_br0360 article-title: The Lyapunov exponent and joint spectral radius of pairs of matrices are hard – when not impossible – to compute and to approximate publication-title: Math. Control Signals Systems doi: 10.1007/BF01219774 – volume: 204 start-page: 1122 issue: 8 year: 2013 ident: 10.1016/j.laa.2016.10.013_br0390 article-title: On the structure of self-affine convex bodies publication-title: Sb. Math. doi: 10.1070/SM2013v204n08ABEH004332 – volume: 428 start-page: 2296 issue: 10 year: 2008 ident: 10.1016/j.laa.2016.10.013_br0150 article-title: Efficient algorithms for deciding the type of growth of products of integer matrices publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2007.08.001 – year: 2002 ident: 10.1016/j.laa.2016.10.013_br0120 – volume: 202 start-page: 1413 issue: 10 year: 2010 ident: 10.1016/j.laa.2016.10.013_br0380 article-title: Self-affine polytopes. Applications to functional equations and matrix theory publication-title: Sb. Math. doi: 10.1070/SM2011v202n10ABEH004193 – start-page: 451 year: 1990 ident: 10.1016/j.laa.2016.10.013_br0340 article-title: Some binary partition functions – volume: 34 start-page: 202 year: 1975 ident: 10.1016/j.laa.2016.10.013_br0240 article-title: The Burnside problem for semigroups publication-title: J. Algebra – volume: 191 start-page: 381 issue: 3–4 year: 2000 ident: 10.1016/j.laa.2016.10.013_br0280 article-title: Asymptotic behavior of the partition function publication-title: Sb. Math. doi: 10.1070/SM2000v191n03ABEH000464 – volume: 50 start-page: 2193 issue: 4 year: 2012 ident: 10.1016/j.laa.2016.10.013_br0090 article-title: A maximum principle for the stability analysis of positive bilinear control systems with applications to positive linear switched systems publication-title: SIAM J. Control Optim. doi: 10.1137/11083808X – volume: 25 start-page: 1433 issue: 5 year: 1994 ident: 10.1016/j.laa.2016.10.013_br0370 article-title: Wavelet analysis of refinement equations publication-title: SIAM J. Math. Anal. doi: 10.1137/S0036141092228179 – volume: 47 start-page: 344 issue: 3 year: 1986 ident: 10.1016/j.laa.2016.10.013_bib4D50s1 article-title: Lyapunov functions, defining necessary and sufficient conditions for the absolute stability of nonlinear nonstationary control systems, I publication-title: Autom. Remote Control – volume: 47 start-page: 1007 year: 1995 ident: 10.1016/j.laa.2016.10.013_br0170 article-title: On permutability and submultiplicativity of spectral radius publication-title: Canad. J. Math. doi: 10.4153/CJM-1995-053-x – year: 2003 ident: 10.1016/j.laa.2016.10.013_br0180 – volume: 47 start-page: 620 issue: 5 year: 1986 ident: 10.1016/j.laa.2016.10.013_bib4D50s3 article-title: Lyapunov functions, defining necessary and sufficient conditions for the absolute stability of nonlinear nonstationary control systems, III publication-title: Autom. Remote Control – year: 2000 ident: 10.1016/j.laa.2016.10.013_br0330 – volume: 70 start-page: 123 issue: 5 year: 2006 ident: 10.1016/j.laa.2016.10.013_br0290 article-title: Fractal curves and wavelets publication-title: Izv. Math. doi: 10.1070/IM2006v070n05ABEH002335 – volume: 166 start-page: 21 year: 1992 ident: 10.1016/j.laa.2016.10.013_br0040 article-title: Bounded semigroups of matrices publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(92)90267-E – volume: 41 start-page: 135 year: 2000 ident: 10.1016/j.laa.2016.10.013_br0050 article-title: The boundedness of all products of a pair of matrices is undecidable publication-title: Systems Control Lett. doi: 10.1016/S0167-6911(00)00049-9 – volume: 5 start-page: 183 year: 1977 ident: 10.1016/j.laa.2016.10.013_br0140 article-title: Un algorithme calculant le cardinal, fini ou infini, des demi-groupes de matrices publication-title: Theoret. Comput. Sci. doi: 10.1016/0304-3975(77)90006-8 – volume: 53 start-page: 55 issue: 1 year: 2012 ident: 10.1016/j.laa.2016.10.013_br0100 article-title: A boundedness criterion for the variations of self-similar functions publication-title: Sib. Math. J. doi: 10.1134/S0037446612010053 – year: 1988 ident: 10.1016/j.laa.2016.10.013_br0030 – volume: 13 start-page: 37 issue: 1 year: 2013 ident: 10.1016/j.laa.2016.10.013_br0110 article-title: Exact computation of joint spectral characteristics of linear operators publication-title: Found. Comput. Math. doi: 10.1007/s10208-012-9121-0 – volume: 18 start-page: 607 issue: 4 year: 2007 ident: 10.1016/j.laa.2016.10.013_br0300 article-title: Spectral decomposition of 2-block Toeplitz matrices and refinement equations publication-title: St. Petersburg Math. J. doi: 10.1090/S1061-0022-07-00963-6 – volume: 61 start-page: 995 issue: 5 year: 1997 ident: 10.1016/j.laa.2016.10.013_br0270 article-title: The generalized spectral radius. A geometric approach publication-title: Izv. Math. doi: 10.1070/IM1997v061n05ABEH000161 |
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| SubjectTerms | Combinatorial analysis Convex body Ellipsoid Euclidean space Finite matrix group Fractal curves Functional equations Joint spectral characteristics Linear algebra Linear switching systems Matrix Multiplicative semigroup Polynomial algorithm Polynomials Spectral radius Theorems |
| Title | Matrix semigroups with constant spectral radius |
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