Geodesic
A class of test Hessenberg matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 89-92

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We present a class of parametric Hessenberg matrices, intended for testing linear-algebraic procedures. Their eigenvalues and subdiagonal elements are arbitrarily prescribed, while the eigenvector and the inverse matrices are computed. 
@article{ZNSL_1981_111_a5,
     author = {L. Yu. Kolotilina},
     title = {A class of test {Hessenberg} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {89--92},
     publisher = {mathdoc},
     volume = {111},
     year = {1981},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a5/}
}
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L. Yu. Kolotilina. A class of test Hessenberg matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 89-92. http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a5/