Rank of Linear and Quadratic Combinations of Matrices

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Ch. R. Johnson
J. M. Pena
T. Szulc


In this paper, the rank of some combinations of matrices is analysed. In particular, the rank of all matrices on the line joining two rank $1$ matrices is characterized, and the rank of convex combinations of two matrices and quadratic combinations of three matrices is studied. Presented results concern the problem of robustness of rank under certain kinds of perturbations of a matrix.

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