The Kahan matrix is also in the MATLAB gallery, and can be created by the command
G = gallery('kahan',N)
Kahan's matrix [2] was devised to illustrate that QR factorisation with column pivoting is not a fail-safe method for determining the rank of the matrix. Rank determination is related to the "distance to singularity" of a matrix [1], or in other words, how large a perturbation is needed to make the matrix singular. The pseudospectra are shown in [3].
[1]: N. J. Higham, "Matrix nearness problems and applications", NA Rep. 161, Dept. of Maths., U. of Manchester, June 1988.
[2]: W. Kahan, "Numerical linear algebra", Canad. Math. Bull. 9, pp. 757-801, 1966.
[3]: L. N. Trefethen, "Psuedospectra of matrices", in "Numerical Analysis 1991" (Dundee 1991), Longman Sci. Tech., Harlow, 1992, 234-266.
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