Singular tuples of matrices is not a null cone (and the symmetries of algebraic varieties)
暂无分享,去创建一个
[1] Harm Derksen,et al. Degree bounds for semi-invariant rings of quivers , 2016, Journal of Pure and Applied Algebra.
[2] Michel Van den Bergh,et al. Semi-invariants of quivers for arbitrary dimension vectors , 1999 .
[3] László Lovász,et al. On determinants, matchings, and random algorithms , 1979, International Symposium on Fundamentals of Computation Theory.
[4] Youming Qiao,et al. Constructive non-commutative rank computation is in deterministic polynomial time , 2015, computational complexity.
[5] J. Dieudonné,et al. Sur une généralisation du groupe orthogonal à quatre variables , 1948 .
[6] Christophe Reutenauer,et al. Inversion height in free fields , 1996 .
[7] Orit E. Raz,et al. Subspace arrangements, graph rigidity and derandomization through submodular optimization , 2019, Bolyai Society Mathematical Studies.
[8] Amir Shpilka,et al. Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing , 2013, APPROX-RANDOM.
[9] Amir Yehudayoff,et al. Arithmetic Circuits: A survey of recent results and open questions , 2010, Found. Trends Theor. Comput. Sci..
[10] M. Panella. Associate Editor of the Journal of Computer and System Sciences , 2014 .
[11] Harm Derksen,et al. Polynomial degree bounds for matrix semi-invariants , 2015, ArXiv.
[12] Peter Bürgisser,et al. Alternating minimization, scaling algorithms, and the null-cone problem from invariant theory , 2017, ITCS.
[13] Mátyás Domokos,et al. Semi-invariants of quivers as determinants , 2001 .
[14] J. Weyman. Cohomology of Vector Bundles and Syzygies , 2003 .
[15] E. B. Dynkin,et al. The maximal subgroups of the classical groups , 1960 .
[16] D. Happel. Relative invariants and subgeneric orbits of quivers of finite and tame type , 1982 .
[17] Avi Wigderson,et al. Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing , 2018, STOC.
[18] R. Meshulam. On k-spaces of real matrices , 1990 .
[19] Ketan Mulmuley,et al. Geometric Complexity Theory I: An Approach to the P vs. NP and Related Problems , 2002, SIAM J. Comput..
[20] Leonid Gurvits,et al. Classical complexity and quantum entanglement , 2004, J. Comput. Syst. Sci..
[21] Ketan Mulmuley,et al. Geometric Complexity Theory V: Efficient algorithms for Noether Normalization , 2012 .
[22] Roy Meshulam,et al. Spaces of Singular Matrices and Matroid Parity , 2002, Eur. J. Comb..
[23] P. Newstead. Moduli Spaces and Vector Bundles: Geometric Invariant Theory , 2009 .
[24] Harm Derksen,et al. Algorithms for orbit closure separation for invariants and semi-invariants of matrices , 2018, ArXiv.
[25] Joe W. Harris,et al. Vector spaces of matrices of low rank , 1988 .
[26] P. Steerenberg,et al. Targeting pathophysiological rhythms: prednisone chronotherapy shows sustained efficacy in rheumatoid arthritis. , 2010, Annals of the rheumatic diseases.
[27] Harm Derksen,et al. Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients , 2000 .
[28] J. M. Landsberg,et al. Geometry and Complexity Theory , 2017 .
[29] B. M. Fulk. MATH , 1992 .
[30] Robert M. Guralnick,et al. Invertible preservers and algebraic groups , 1994 .
[31] Cole Franks. Operator scaling with specified marginals , 2018, STOC.
[32] J. Urry. Complexity , 2006, Interpreting Art.
[33] Youming Qiao,et al. Non-commutative Edmonds’ problem and matrix semi-invariants , 2015, computational complexity.
[34] Visu Makam. Hilbert series and degree bounds for matrix (semi-)invariants , 2015 .
[35] Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing , 2018, STOC.
[36] Leslie G. Valiant,et al. The Complexity of Computing the Permanent , 1979, Theor. Comput. Sci..
[37] Russell Impagliazzo,et al. Derandomizing Polynomial Identity Tests Means Proving Circuit Lower Bounds , 2003, STOC '03.
[38] 유재철,et al. Randomization , 2020, Randomization, Bootstrap and Monte Carlo Methods in Biology.
[39] James S. Milne,et al. Algebraic Groups: The Theory of Group Schemes of Finite Type over a Field , 2017 .
[40] Harm Derksen,et al. On non-commutative rank and tensor rank , 2016, 1606.06701.
[41] R. Meshulam. ON THE MAXIMAL RANK IN A SUBSPACE OF MATRICES , 1985 .
[42] Harm Derksen,et al. Generating invariant rings of quivers in arbitrary characteristic , 2016, 1610.06617.
[43] J. Edmonds. Systems of distinct representatives and linear algebra , 1967 .
[44] Chi-Kwong Li,et al. Overgroups of some classical linear groups with applications to linear preserver problems , 1994 .
[45] Avi Wigderson,et al. Efficient Algorithms for Tensor Scaling, Quantum Marginals, and Moment Polytopes , 2018, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science (FOCS).
[46] R. Tennant. Algebra , 1941, Nature.
[47] D. Happel. Relative invariants of quivers of tame type , 1984 .
[48] Avi Wigderson,et al. Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via Operator Scaling , 2018 .
[49] J. A. Rodríguez,et al. Linear and Multilinear Algebra , 2007 .
[50] S. A. Amitsur. Rational identities and applications to algebra and geometry , 1966 .
[51] Ketan Mulmuley,et al. Geometric Complexity Theory II: Towards Explicit Obstructions for Embeddings among Class Varieties , 2006, SIAM J. Comput..
[52] Avi Wigderson,et al. A Deterministic Polynomial Time Algorithm for Non-commutative Rational Identity Testing , 2015, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).
[53] Christophe Reutenauer,et al. COMMUTATIVE/NONCOMMUTATIVE RANK OF LINEAR MATRICES AND SUBSPACES OF MATRICES OF LOW RANK , 2004 .
[54] Chi-Kwong Li,et al. Linear Preserver Problems , 2001, Am. Math. Mon..