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The rigidity of a matrix M is the function R M (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 lineardoi:10.1016/s0024-3795(99)00225-6 fatcat:t7fclqerxjcgncwwlllbg2hfce