Degree complexity of birational maps related to matrix inversion: symmetric case

Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Truong, Tuyen Trung [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2010

Schlagwörter:	Birational mappings Degree complexity Matrix inversion Symmetric matrices

Anmerkung:	© Springer-Verlag 2010

Übergeordnetes Werk:	Enthalten in: Mathematische Zeitschrift - Berlin : Springer, 1918, 270(2010), 3-4 vom: 05. Dez., Seite 725-738
Übergeordnetes Werk:	volume:270 ; year:2010 ; number:3-4 ; day:05 ; month:12 ; pages:725-738

Links:	Volltext

DOI / URN:	10.1007/s00209-010-0821-3

Katalog-ID:	SPR001920146

Internformat


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520			\|a Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006).
650		4	\|a Birational mappings \|7 (dpeaa)DE-He213
650		4	\|a Degree complexity \|7 (dpeaa)DE-He213
650		4	\|a Matrix inversion \|7 (dpeaa)DE-He213
650		4	\|a Symmetric matrices \|7 (dpeaa)DE-He213
773	0	8	\|i Enthalten in \|t Mathematische Zeitschrift \|d Berlin : Springer, 1918 \|g 270(2010), 3-4 vom: 05. Dez., Seite 725-738 \|w (DE-627)254630812 \|w (DE-600)1462134-4 \|x 1432-1823 \|7 nnns
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856	4	0	\|u https://dx.doi.org/10.1007/s00209-010-0821-3 \|z lizenzpflichtig \|3 Volltext
912			\|a GBV_USEFLAG_A
912			\|a SYSFLAG_A
912			\|a GBV_SPRINGER
912			\|a GBV_ILN_11
912			\|a GBV_ILN_20
912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2018
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
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Indexfelder

author_variant	t t t tt ttt
matchkey_str	article:14321823:2010----::ereopeiyfiainlaseaetmtiiv
hierarchy_sort_str	2010
publishDate	2010
allfields	10.1007/s00209-010-0821-3 doi (DE-627)SPR001920146 (SPR)s00209-010-0821-3-e DE-627 ger DE-627 rakwb eng Truong, Tuyen Trung verfasserin aut Degree complexity of birational maps related to matrix inversion: symmetric case 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). Birational mappings (dpeaa)DE-He213 Degree complexity (dpeaa)DE-He213 Matrix inversion (dpeaa)DE-He213 Symmetric matrices (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 270(2010), 3-4 vom: 05. Dez., Seite 725-738 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:270 year:2010 number:3-4 day:05 month:12 pages:725-738 https://dx.doi.org/10.1007/s00209-010-0821-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 270 2010 3-4 05 12 725-738
spelling	10.1007/s00209-010-0821-3 doi (DE-627)SPR001920146 (SPR)s00209-010-0821-3-e DE-627 ger DE-627 rakwb eng Truong, Tuyen Trung verfasserin aut Degree complexity of birational maps related to matrix inversion: symmetric case 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). Birational mappings (dpeaa)DE-He213 Degree complexity (dpeaa)DE-He213 Matrix inversion (dpeaa)DE-He213 Symmetric matrices (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 270(2010), 3-4 vom: 05. Dez., Seite 725-738 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:270 year:2010 number:3-4 day:05 month:12 pages:725-738 https://dx.doi.org/10.1007/s00209-010-0821-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 270 2010 3-4 05 12 725-738
allfields_unstemmed	10.1007/s00209-010-0821-3 doi (DE-627)SPR001920146 (SPR)s00209-010-0821-3-e DE-627 ger DE-627 rakwb eng Truong, Tuyen Trung verfasserin aut Degree complexity of birational maps related to matrix inversion: symmetric case 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). Birational mappings (dpeaa)DE-He213 Degree complexity (dpeaa)DE-He213 Matrix inversion (dpeaa)DE-He213 Symmetric matrices (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 270(2010), 3-4 vom: 05. Dez., Seite 725-738 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:270 year:2010 number:3-4 day:05 month:12 pages:725-738 https://dx.doi.org/10.1007/s00209-010-0821-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 270 2010 3-4 05 12 725-738
allfieldsGer	10.1007/s00209-010-0821-3 doi (DE-627)SPR001920146 (SPR)s00209-010-0821-3-e DE-627 ger DE-627 rakwb eng Truong, Tuyen Trung verfasserin aut Degree complexity of birational maps related to matrix inversion: symmetric case 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). Birational mappings (dpeaa)DE-He213 Degree complexity (dpeaa)DE-He213 Matrix inversion (dpeaa)DE-He213 Symmetric matrices (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 270(2010), 3-4 vom: 05. Dez., Seite 725-738 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:270 year:2010 number:3-4 day:05 month:12 pages:725-738 https://dx.doi.org/10.1007/s00209-010-0821-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 270 2010 3-4 05 12 725-738
allfieldsSound	10.1007/s00209-010-0821-3 doi (DE-627)SPR001920146 (SPR)s00209-010-0821-3-e DE-627 ger DE-627 rakwb eng Truong, Tuyen Trung verfasserin aut Degree complexity of birational maps related to matrix inversion: symmetric case 2010 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer-Verlag 2010 Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). Birational mappings (dpeaa)DE-He213 Degree complexity (dpeaa)DE-He213 Matrix inversion (dpeaa)DE-He213 Symmetric matrices (dpeaa)DE-He213 Enthalten in Mathematische Zeitschrift Berlin : Springer, 1918 270(2010), 3-4 vom: 05. Dez., Seite 725-738 (DE-627)254630812 (DE-600)1462134-4 1432-1823 nnns volume:270 year:2010 number:3-4 day:05 month:12 pages:725-738 https://dx.doi.org/10.1007/s00209-010-0821-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 270 2010 3-4 05 12 725-738
language	English
source	Enthalten in Mathematische Zeitschrift 270(2010), 3-4 vom: 05. Dez., Seite 725-738 volume:270 year:2010 number:3-4 day:05 month:12 pages:725-738
sourceStr	Enthalten in Mathematische Zeitschrift 270(2010), 3-4 vom: 05. Dez., Seite 725-738 volume:270 year:2010 number:3-4 day:05 month:12 pages:725-738
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Birational mappings Degree complexity Matrix inversion Symmetric matrices
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container_title	Mathematische Zeitschrift
authorswithroles_txt_mv	Truong, Tuyen Trung @@aut@@
publishDateDaySort_date	2010-12-05T00:00:00Z
hierarchy_top_id	254630812
id	SPR001920146
language_de	englisch
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author	Truong, Tuyen Trung
spellingShingle	Truong, Tuyen Trung misc Birational mappings misc Degree complexity misc Matrix inversion misc Symmetric matrices Degree complexity of birational maps related to matrix inversion: symmetric case
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topic_title	Degree complexity of birational maps related to matrix inversion: symmetric case Birational mappings (dpeaa)DE-He213 Degree complexity (dpeaa)DE-He213 Matrix inversion (dpeaa)DE-He213 Symmetric matrices (dpeaa)DE-He213
topic	misc Birational mappings misc Degree complexity misc Matrix inversion misc Symmetric matrices
topic_unstemmed	misc Birational mappings misc Degree complexity misc Matrix inversion misc Symmetric matrices
topic_browse	misc Birational mappings misc Degree complexity misc Matrix inversion misc Symmetric matrices
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title	Degree complexity of birational maps related to matrix inversion: symmetric case
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title_full	Degree complexity of birational maps related to matrix inversion: symmetric case
author_sort	Truong, Tuyen Trung
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author-letter	Truong, Tuyen Trung
doi_str_mv	10.1007/s00209-010-0821-3
title_sort	degree complexity of birational maps related to matrix inversion: symmetric case
title_auth	Degree complexity of birational maps related to matrix inversion: symmetric case
abstract	Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). © Springer-Verlag 2010
abstractGer	Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). © Springer-Verlag 2010
abstract_unstemmed	Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. (J Phys A Math Gen 39:3641–3654, 2006). © Springer-Verlag 2010
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title_short	Degree complexity of birational maps related to matrix inversion: symmetric case
url	https://dx.doi.org/10.1007/s00209-010-0821-3
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doi_str	10.1007/s00209-010-0821-3
up_date	2024-07-04T00:59:46.059Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR001920146</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327145300.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2010 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00209-010-0821-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR001920146</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00209-010-0821-3-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Truong, Tuyen Trung</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Degree complexity of birational maps related to matrix inversion: symmetric case</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2010</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer-Verlag 2010</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract For q ≥ 3, we let %${\mathcal{S}_q}%$ denote the projectivization of the set of symmetric q × q matrices with coefficients in %${\mathbb{C}}%$. We let %${I(x)=(x_{i,j})^{-1}}%$ denote the matrix inverse, and we let %${J(x)=(x_{i,j}^{-1})}%$ be the matrix whose entries are the reciprocals of the entries of x. We let %${K\|\mathcal{S}_q=I\circ J:~\mathcal{S}_q\rightarrow \mathcal{S}_q}%$ denote the restriction of the composition I ◦ J to %${\mathcal{S}_q}%$. This is a birational map whose properties have attracted some attention in statistical mechanics. In this paper we compute the degree complexity of %${K\|\mathcal{S}_q}%$, thus confirming a conjecture of Angles d’Auriac et al. 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Degree complexity of birational maps related to matrix inversion: symmetric case

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