Geodesic
A class of test Hessenberg matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part V, Tome 111 (1981), pp. 89-92 
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/
@article{ZNSL_1981_111_a5,
     author = {L. Yu. Kolotilina},
     title = {A class of test {Hessenberg} matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {89--92},
     year = {1981},
     volume = {111},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1981_111_a5/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.