... that's nothing new. the point was to address a related question: suppose that the eigensystem {v_i, λ_i}, i = 1, ..., n of a full-rank, well-conditioned n-by-n square matrix A is known, and then you are given a related matrix B = A + E, where E represents some type of random noise. Can a relationship between E and c be derived, such that the eigensystem of A also satisfies f( B v_i - λ_i v_i ) <= c, for all i and some f?

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