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Abstract: The rigidity of a matrix M is the function RM (r), which, for a given r, gives the minimum number of entries of M which one has to change in order to reduce its rank to at most r. This notion has been introduced by Valiant in 1977 in connection with the complexity of computing linear forms. Despite more than 20 years of research, very little is known about the rigidity of matrices. Nonlinear lower bounds on matrix rigidity would lead to new lower bound techniques for the computation of... (Update)
Context of citations to this paper: More
...the original papers by Shannon and Lov asz. Matrix rigidity has been introduced in [22] A survey of both results and open questions is [7]. References [5, 17, 2] contain results on properties of low rank matrices with applications to matrix rigidity and show the connections...
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BibTeX entry: (Update)
B.Codenotti, "Matrix Rigidity", Linear Algebra and its Applications, 304 (1-3) (2000), 181--192. http://citeseer.ist.psu.edu/codenotti99matrix.html More
@article{ codenotti00matrix,
author = "Bruno Codenotti",
title = "Matrix rigidity",
journal = "Linear Algebra and its Applications",
volume = "304",
number = "1--3",
pages = "181--192",
year = "2000",
url = "citeseer.ist.psu.edu/codenotti99matrix.html" }
Citations (may not include all citations):193 Extremal graph theory (context) - Bollob'as - 1978
41 Graph theoretic arguments in low-level complexity (context) - Valiant - 1977
27 The variation of the spectrum of a normal matrix (context) - Hoffman, Wielandt - 1953
20 Graph-Theoretic properties in Computational Complexity (context) - Valiant - 1976
20 A note on matrix rigidity (context) - Friedman - 1993
16 tensor ranks and communication complexity (context) - Pudl'ak, odl et al. - 1997
15 The smallest perturbation of a submatrix which lowers the ra.. (context) - Demmel - 1987
15 Johns Hopkins Series in the Mathematical Sciences (context) - Golub, Van Loan - 1983
14 Applications of Matrix Methods to the Theory of Lower Bounds.. (context) - Razborov - 1990
14 Why is Boolean complexity theory difficult - Valiant - 1992
11 A Spectral Approach to Lower Bounds (context) - Chazelle - 1994
10 Note on a Lower Bound on the Linear Complexity of the Fast F.. (context) - Morgenstern - 1973
8 Improved Lower Bounds on the Rigidity of Hadamard Matrices P.. - Kashin, Razborov - 1997
6 the Complexity of Bilinear Forms - Nisan, Wigderson - 1995
6 Communication in bounded depth circuits - Pudl'ak - 1994
6 Some structural properties of low rank matrices related to c.. - Codenotti, Pudl'ak et al.
5 Some combinatorial-algebraic problems from complexity theory (context) - Pudl'ak, odl - 1994
5 On sparse graphs with dense long paths (context) - Erdos, Graham et al. - 1975
4 Information Processing Letters (context) - Shokrollahi, Spielman et al. - 1998
3 The Linear Complexity of Computation (context) - Morgenstern - 1975
3 A Generalization of the EckartYoung -Mirsky Approximation Th.. (context) - Golub, Hoffman et al. - 1988
3 Using the notion of separability and independence for provin.. (context) - Yu - 1976
2 A Note on the Use of Determinant for Proving Lower Bounds on.. (context) - Pudl'ak - 1998
2 The smallest perturbation of a submatrix which lowers the ra.. (context) - Watson - 1988
1 On some properties of the matrices of bounded operators from.. (context) - Kashin - 1980
1 the Rigidity of Hadamard Matrices (context) - Alon
1 Mathematical Notes of the Russian Academy of Sciences (context) - Lunin, norms - 1989
1 Spectral Methods for Matrix Rigidity with Applications to Si.. - Satyanarayana - 1995
1 Some remarks on the restriction of operators to coordinate s.. (context) - Kashin, Tzaffiri - 1993
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