The "Godunov matrix" is a 7 x 7 matrix that has been used by S. K. Godunov to illustrate the difficulty of computing certain eigenvalues in floating point arithmetic [1]. The entries of A are integers and the exact eigenvalues are -4, -2, -1, 0, 1, 2, 4. This can be seen from the fact that L*A/L is upper triangular, where L is the lower-triangular matrix defined by
L = eye(7); L(3,1) = 1; L(6,1) = 1;L(5,3) = 1; L(7,[2 3 5]) = 1;
[1]: S. K. Godunov, "Modern Aspects of Linear Algebra", Translations of Mathematical Monographs v. 175, Amer. Math. Soc., Providence, RI, 1998.
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