This is Demmel's matrix, which was perhaps the first matrix whose pseudospectra (with N=3) appeared in a published paper [1]. Demmel devised the matrix in order to disprove a conjecture of Van Loan's [2].
[1]: J. W. Demmel, "A counterexample for two conjectures about stability", IEEE Trans. Auto. Control, AC-32, pp. 340-343, 1987.
[2]: C. Van Loan, "How near is a stable matrix to an unstable matrix?", in R. Brualdi, et al., eds, Contemporary Mathematics 47, Amer. Math. Soc., 1985
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