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
Autor*in: |
Truong, Tuyen Trung [verfasserIn] |
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Format: |
E-Artikel |
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Sprache: |
Englisch |
Erschienen: |
2010 |
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Anmerkung: |
© Springer-Verlag 2010 |
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Übergeordnetes Werk: |
Enthalten in: Mathematische Zeitschrift - Berlin : Springer, 1918, 270(2010), 3-4 vom: 05. Dez., Seite 725-738 |
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Übergeordnetes Werk: |
volume:270 ; year:2010 ; number:3-4 ; day:05 ; month:12 ; pages:725-738 |
Links: |
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DOI / URN: |
10.1007/s00209-010-0821-3 |
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Katalog-ID: |
SPR001920146 |
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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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912 | |a GBV_SPRINGER | ||
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912 | |a GBV_ILN_170 | ||
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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 | ||
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912 | |a GBV_ILN_2001 | ||
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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 | ||
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912 | |a GBV_ILN_2070 | ||
912 | |a GBV_ILN_2086 | ||
912 | |a GBV_ILN_2088 | ||
912 | |a GBV_ILN_2093 | ||
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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 | ||
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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 | ||
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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 |
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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 |
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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 |
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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 |
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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 |
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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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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 |
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Degree complexity of birational maps related to matrix inversion: symmetric case |
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degree complexity of birational maps related to matrix inversion: symmetric case |
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Degree complexity of birational maps related to matrix inversion: symmetric case |
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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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Degree complexity of birational maps related to matrix inversion: symmetric case |
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<?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. (J Phys A Math Gen 39:3641–3654, 2006).</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Birational mappings</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Degree complexity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Matrix inversion</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Symmetric matrices</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Mathematische Zeitschrift</subfield><subfield code="d">Berlin : Springer, 1918</subfield><subfield code="g">270(2010), 3-4 vom: 05. Dez., Seite 725-738</subfield><subfield code="w">(DE-627)254630812</subfield><subfield code="w">(DE-600)1462134-4</subfield><subfield code="x">1432-1823</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:270</subfield><subfield code="g">year:2010</subfield><subfield code="g">number:3-4</subfield><subfield code="g">day:05</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:725-738</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00209-010-0821-3</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield 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