Ballico, Edoardo Typical labels of real forms. (English) Zbl 1521.14094 Riv. Mat. Univ. Parma (N.S.) 14, No. 1, 87-95 (2023). MSC: 14N05 15A69 × Cite Format Result Cite Review PDF Full Text: Link
Brambilla, Maria Chiara; Staglianò, Giovanni Algebraic boundaries among typical ranks for real binary forms of arbitrary degree. (English) Zbl 1482.14053 Found. Comput. Math. 21, No. 4, 1003-1022 (2021). Reviewer: Vincenzo Galgano (Povo) MSC: 14N07 14P10 15A69 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sumi, Toshio; Miyazaki, Mitsuhiro; Sakata, Toshio Typical ranks of semi-tall real 3-tensors. (English) Zbl 1470.15020 Linear Multilinear Algebra 69, No. 9, 1734-1746 (2021). MSC: 15A69 15A03 14P10 14M12 13C40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bernstein, Daniel Irving; Blekherman, Grigoriy; Lee, Kisun Typical ranks in symmetric matrix completion. (English) Zbl 1459.15029 J. Pure Appl. Algebra 225, No. 7, Article ID 106603, 17 p. (2021). MSC: 15A83 14Q30 62R01 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ballico, Edoardo Partially complex ranks for real projective varieties. (English) Zbl 1460.14117 Riv. Mat. Univ. Parma (N.S.) 11, No. 2, 207-216 (2020). MSC: 14N07 15A69 14P05 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Ballico, Edoardo; Ventura, Emanuele Labels of real projective varieties. (English) Zbl 1439.14166 Boll. Unione Mat. Ital. 13, No. 2, 257-273 (2020). MSC: 14P10 14N05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bernstein, Daniel Irving; Blekherman, Grigoriy; Sinn, Rainer Typical and generic ranks in matrix completion. (English) Zbl 1425.15024 Linear Algebra Appl. 585, 71-104 (2020). MSC: 15A83 05C50 14P05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Brambilla, Maria Chiara; Staglianò, Giovanni On the algebraic boundaries among typical ranks for real binary forms. (English) Zbl 1397.15021 Linear Algebra Appl. 557, 403-418 (2018). MSC: 15A69 14P10 14N05 11E16 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Miyazaki, Mitsuhiro; Sumi, Toshio; Sakata, Toshio Typical ranks of certain 3-tensors and absolutely full column rank tensors. (English) Zbl 1386.15050 Linear Multilinear Algebra 66, No. 1, 193-205 (2018). MSC: 15A69 15A15 65F40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sumi, Toshio; Miyazaki, Mitsuhiro; Sakata, Toshio Typical ranks for 3-tensors, nonsingular bilinear maps and determinantal ideals. (English) Zbl 1353.15002 J. Algebra 471, 409-453 (2017). MSC: 15A03 15A69 13C40 14M12 14P10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Qi, Yang; Comon, Pierre; Lim, Lek-Heng Semialgebraic geometry of nonnegative tensor rank. (English) Zbl 1349.14183 SIAM J. Matrix Anal. Appl. 37, No. 4, 1556-1580 (2016). MSC: 14P10 15A69 41A50 41A52 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Blekherman, Grigoriy; Sinn, Rainer Real rank with respect to varieties. (English) Zbl 1360.15028 Linear Algebra Appl. 505, 344-360 (2016). MSC: 15A69 15A21 14P05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Banchi, Maurizio Rank and border rank of real ternary cubics. (English) Zbl 1332.15058 Boll. Unione Mat. Ital. 8, No. 1, 65-80 (2015). Reviewer: Pasha Zusmanovich (Ostrava) MSC: 15A72 14H45 15A03 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sumi, Toshio; Miyazaki, Mitsuhiro; Sakata, Toshio Typical ranks of \(m\times n\times(m-1)n\) tensors with \(3\leq m\leq n\) over the real number field. (English) Zbl 1310.15043 Linear Multilinear Algebra 63, No. 5, 940-955 (2015). Reviewer: A. Arvanitoyeorgos (Patras) MSC: 15A69 14P10 14Q20 15A03 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sumi, Toshio; Sakata, Toshio; Miyazaki, Mitsuhiro Rank of \(n\)-tensors with size \(2\times \cdots\times 2\). (English) Zbl 1315.15025 Far East J. Math. Sci. (FJMS) 90, No. 2, 141-162 (2014). Reviewer: Hans Havlicek (Wien) MSC: 15A69 14P10 14Q20 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Ballico, Edoardo On the typical rank of real polynomials (or symmetric tensors) with a fixed border rank. (English) Zbl 1308.14054 Acta Math. Vietnam. 39, No. 3, 367-378 (2014). MSC: 14N05 14Q05 15A69 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ballico, Edoardo On the typical rank of real bivariate polynomials. (English) Zbl 1302.14043 Linear Algebra Appl. 452, 263-269 (2014). MSC: 14N05 15A69 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sumi, Toshio; Sakata, Toshio; Miyazaki, Mitsuhiro Typical ranks for \(m\times n\times (m-1)n\) tensors with \(m \leq n\). (English) Zbl 1260.15042 Linear Algebra Appl. 438, No. 2, 953-958 (2013). Reviewer: Grozio Stanilov (Sofia) MSC: 15A69 15A72 15A03 × Cite Format Result Cite Review PDF Full Text: DOI
Bergqvist, Göran Exact probabilities for typical ranks of \(2 \times 2 \times 2\) and \(3 \times 3 \times 2\) tensors. (English) Zbl 1266.15037 Linear Algebra Appl. 438, No. 2, 663-667 (2013). Reviewer: Manouchehr Misaghian (Prairie View) MSC: 15A69 15B52 × Cite Format Result Cite Review PDF Full Text: DOI
Friedland, Shmuel On the generic and typical ranks of 3-tensors. (English) Zbl 1237.15020 Linear Algebra Appl. 436, No. 3, 478-497 (2012). Reviewer: Pasha Zusmanovich (Tallinn) MSC: 15A69 14A25 14P10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bergqvist, Göran; Forrester, Peter J. Rank probabilities for real random \(N\times N \times 2\) tensors. (English) Zbl 1245.15036 Electron. Commun. Probab. 16, 630-637 (2011). MSC: 15B52 15A69 60B20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Causa, A.; Re, R. On the maximum rank of a real binary form. (English) Zbl 1222.14123 Ann. Mat. Pura Appl. (4) 190, No. 1, 55-59 (2011). Reviewer: Maria Chiara Brambilla (Ancona) MSC: 14P05 14N05 15A21 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
ten Berge, Jos M. F. Simplicity and typical rank results for three-way arrays. (English) Zbl 1208.62181 Psychometrika 76, No. 1, 3-12 (2011). MSC: 62H25 15A69 15A99 × Cite Format Result Cite Review PDF Full Text: DOI
Tendeiro, Jorge N.; ten Berge, Jos M. F.; Kiers, Henk A. L. Simplicity transformations for three-way arrays with symmetric slices, and applications to Tucker-3 models with sparse core arrays. (English) Zbl 1274.62413 Linear Algebra Appl. 430, No. 4, 924-940 (2009). MSC: 62H25 15A04 15A69 × Cite Format Result Cite Review PDF Full Text: DOI Link
Ten Berge, Jos M. F.; Stegeman, Alwin; Dosse, Mohammed Bennani The Carroll and Chang conjecture of equal Indscal components when Candecomp/Parafac gives perfect fit. (English) Zbl 1185.65073 Linear Algebra Appl. 430, No. 2-3, 818-829 (2009). MSC: 65F30 62H25 15A69 × Cite Format Result Cite Review PDF Full Text: DOI
Ten Berge, Jos M. F.; Stegeman, Alwin Symmetry transformations for square sliced three-way arrays, with applications to their typical rank. (English) Zbl 1104.15022 Linear Algebra Appl. 418, No. 1, 215-224 (2006). Reviewer: Václav Burjan (Praha) MSC: 15A69 15A03 × Cite Format Result Cite Review PDF Full Text: DOI
ten Berge, Jos M. F.; Sidiropoulos, Nikolaos D.; Rocci, Roberto Typical rank and indscal dimensionality for symmetric three-way arrays of order \(I\times 2\times 2\) or \(I\times 3\times 3\). (English) Zbl 1057.15002 Linear Algebra Appl. 388, 363-377 (2004). Reviewer: Václav Burjan (Praha) MSC: 15A03 62H25 × Cite Format Result Cite Review PDF Full Text: DOI
Catalisano, M. V.; Geramita, A. V.; Gimigliano, A. Ranks of tensors, secant varieties of Segre varieties and fat points. (English) Zbl 1059.14061 Linear Algebra Appl. 355, No. 1-3, 263-285 (2002). Reviewer: Caterina Cumino (Torino) MSC: 14N05 15A69 13D40 × Cite Format Result Cite Review PDF Full Text: DOI
Pengpan, Teparksorn Kostant’s cubic Dirac operator of Lie superalgebras. (English) Zbl 1015.17004 J. Math. Phys. 40, No. 12, 6577-6588 (1999). MSC: 17B10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ten Berge, Jos M. F.; Kiers, Henk A. L. Simplicity of core arrays in three-way principal component analysis and the typical rank of \(p\times q\times 2\) arrays. (English) Zbl 0931.62050 Linear Algebra Appl. 294, No. 1-3, 169-179 (1999). MSC: 62H25 × Cite Format Result Cite Review PDF Full Text: DOI